Fuzzy Multi-Criteria Decision-Making for Oil-Refining Unit Control: Methods, Applications, and Future Directions

Abstract

This article provides a comprehensive exploration of Fuzzy Multi-Criteria Decision-Making (FMCDM) applications for controlling and optimizing oil-refining units. It establishes the foundational principles of fuzzy logic in handling operational uncertainty and incomplete data prevalent in refinery processes. The content details specific FMCDM methodologies like Fuzzy TOPSIS, Disc Spherical Fuzzy Sets (D-SFSs), and hybrid models, illustrating their application through case studies on crude oil pretreatment and stabilization column control. It further addresses troubleshooting and optimization strategies for managing conflicting objectives and data scarcity, and validates these approaches through comparative analysis with conventional methods. Concluding with a forward-looking perspective, the article synthesizes key takeaways and suggests future research directions, including the integration of predictive machine learning models and advanced fuzzy sets for enhanced decision support in petroleum refining.

Fundamentals of Fuzzy Logic and MCDM in Oil-Refining Contexts

Multi-criteria decision-making (MCDM) methodologies are increasingly vital for addressing complex optimization challenges in oil refining processes. This technical note explores the fundamental challenges and solutions for implementing fuzzy MCDM in refinery operations, where processes are characterized by inherent uncertainties, conflicting objectives, and vague or incomplete information. We present structured protocols for applying fuzzy MCDM techniques to specific refining unit operations, including crude oil pretreatment, demulsifier selection, and operating mode optimization for stabilization columns. The provided frameworks enable researchers to systematically integrate expert knowledge with mathematical modeling to achieve optimized operational outcomes under uncertainty.

Theoretical Foundations of Fuzzy MCDM in Refining

Oil refining constitutes a complex chemical-technological system (CTS) with numerous interconnected units characterized by multiple parameters whose influence on operating modes and product quality is often non-formalizable and fuzzy [1]. Traditional optimization approaches frequently fail to capture the inherent uncertainties present in refinery process data and expert judgments.

Fuzzy set theory enhances MCDM by systematically quantifying and processing this linguistic uncertainty, allowing decision-makers to incorporate experiential knowledge from plant operators and process engineers into mathematical models. Unlike conventional approaches that transform fuzzy problems into sets of crisp problems at α-levels—potentially losing important original fuzzy information—recent advances maintain the integrity of fuzzy data throughout the optimization process, leading to more adequate solutions in fuzzy environments [1].

The fundamental MCDM challenge in refining involves identifying optimal solutions that simultaneously satisfy multiple, often competing criteria such as separation efficiency, operational costs, environmental impact, energy consumption, and equipment reliability. Fuzzy MCDM methodologies provide structured approaches to balance these conflicting objectives while accommodating the imperfect information characteristic of real-world refinery operations.

Application Note: Fuzzy MCDM for Specific Refining Challenges

Crude Oil Pretreatment Using Disc Spherical Fuzzy Sets

Background: Crude oil pretreatment is a critical initial refining stage that significantly impacts downstream process efficiency and product quality. Selecting optimal pretreatment strategies involves evaluating multiple technical parameters under uncertainty.

Methodology: The Disc Spherical Fuzzy Sets (D-SFSs) framework within the Aczel-Alsina norm provides an advanced mathematical structure for handling three-dimensional uncertainty (membership, non-membership, and hesitancy) in pretreatment decisions [2]. This approach incorporates circular components to the dimensions of abstention, non-belonging, and belonging, enhancing the framework's adaptability and representational power for complex refinery decisions.

Implementation: Researchers have successfully applied a hybrid MEREC-SWARA-MARCOS-D-SFSs Multiple Attribute Group Decision Making method for crude oil pretreatment optimization [2]. This integrated approach:

• Calculates objective criteria weights using the MEREC (Method based on the Removal Effects of Criteria) technique
• Determines subjective criteria weights through SWARA (Step-wise Weight Assessment Ratio Analysis) methodology
• Generates combined criteria weights and ranks alternatives using the MARCOS (Measurement of Alternatives and Ranking according to Compromise Solution) method

Outcomes: Case studies demonstrate that this approach achieves a 95% reduction in water content and up to 90% reduction in contaminants, while simultaneously reducing energy consumption by 20% during pretreatment operations [2].

Demulsifier Selection Using Fuzzy TOPSIS

Background: Effective separation of water from crude oil via demulsification is essential for maintaining oil quality, optimizing production efficiency, and minimizing operational challenges. Selecting optimal demulsifiers requires balancing multiple competing criteria.

Experimental Protocol:

Table 1: Demulsifier Evaluation Criteria and Metrics

Criterion	Sub-criteria	Measurement Method
Separation Efficiency	Water removal percentage, Separation time	Bottle test, Centrifugal separation analysis
Environmental Impact	Toxicity, Biodegradability	Regulatory screening, OECD biodegradability tests
Cost Effectiveness	Chemical cost, Dosage requirement	Cost-benefit analysis, Dosage optimization studies
Operational Feasibility	Compatibility, Handling safety	Compatibility testing, Safety data sheet analysis

Methodology: The Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS) ranks demulsifiers based on their relative closeness to an ideal solution while incorporating fuzzy linguistic assessments from multiple experts [3].

Application Workflow:

• Criteria Identification: Establish evaluation criteria (separation efficiency, environmental impact, cost, operational feasibility)
• Expert Evaluation: Collect fuzzy assessments from refinery process engineers and chemists
• Weight Assignment: Determine criterion importance weights through pairwise comparisons
• Fuzzy Matrix Construction: Build decision matrix with fuzzy evaluations for each demulsifier against all criteria
• Similarity Calculation: Compute closeness coefficients to ideal and negative-ideal solutions
• Ranking: Prioritize demulsifiers based on descending closeness coefficient values

Results: Application to four commercial demulsifiers (Alcopol 500, Polymer-based Demulsifier, Nalco Champion EC7135A, and Schlumberger's ClearPhase) identified Nalco Champion EC7135A as optimal with a closeness coefficient of 0.751, followed by Alcopol 500 (0.708), Polymer-based Demulsifier (0.692), and Schlumberger's ClearPhase (0.619) [3].

Stabilization Column Optimization via Heuristic Fuzzy Methods

Background: Stabilization columns in primary oil-refining units present complex control challenges due to multivariate interactions and fuzzy operational information.

Methodology: Heuristic fuzzy MCDM methods based on modified optimality principles enable effective decision-making for stabilization column parameter optimization [1] [4]. These approaches combine system models with knowledge and experience of decision-makers (DM) for iterative improvement of operating decisions.

Implementation Framework:

• Develop statistical and fuzzy models of the stabilization column based on experimental-statistical methods and expert evaluations
• Formulate two-criterion optimization problems for column parameters in a fuzzy environment
• Apply heuristic methods based on main criterion and maximin principles to identify compromise solutions
• Validate model effectiveness through comparison with known methods and operational data

Advantages: The developed heuristic methods differ from conventional approaches by making adequate decisions in fuzzy environments through maximized utilization of collected fuzzy information, without requiring transformation into equivalent crisp problems [1].

Experimental Protocols

Protocol 1: Fuzzy Risk Assessment for Refinery Process Operations

Objective: Implement fuzzy logic system (FLS) for risk modeling of process operations to prioritize maintenance activities and risk reduction decisions [5].

Table 2: Risk Assessment Factors for Refinery Assets

Risk Factor	Components	Assessment Scale
Failure Frequency	Historical failure data, Equipment condition	Very low to very high (fuzzy scale)
Safety Impact	Potential injuries, Severity of accidents	Negligible to catastrophic (fuzzy scale)
Environmental Impact	Spill potential, Emission consequences	Insignificant to severe (fuzzy scale)
Operational Impact	Downtime duration, Production loss	Minimal to extensive (fuzzy scale)
Maintenance Cost	Repair expense, Spare part requirements	Very low to very high (fuzzy scale)

Procedure:

• Asset Identification: Catalog critical process assets (e.g., condensers, pumps, compressors)
• Failure Mode Analysis: Identify potential failure modes for each asset
• Fuzzy Assessment: Collect expert evaluations for each risk factor using fuzzy linguistic variables
• Risk Aggregation: Apply fuzzy inference system (Mamdani algorithm) to compute unified risk numbers
• Criticality Classification: Categorize assets as non-critical, semi-critical, or critical based on unified risk thresholds
• Maintenance Prioritization: Schedule inspection and maintenance activities based on risk prioritization

Validation: Comparative analysis demonstrates that fuzzy risk modeling provides better fit to operational data than traditional risk-based maintenance (RBM) methods, with identified failures showing 3 semi-critical and 23 non-critical failures in gas plant case study [5].

Protocol 2: Rankability-Based Weighting for Supplier Selection

Objective: Implement rankability-based weighting method for MCDM problems to overcome contradictions in decision-making while reducing dimensionality of evaluation data [6].

Procedure:

• Data Collection: Gather performance data for alternatives (suppliers, technologies, materials) across multiple criteria
• Spectral Analysis: Perform spectral analysis of the Laplacian matrix derived from decision data
• Weight Aggregation: Create aggregated weights incorporating decision-maker performance, edge weight basis of digraph, and dominance relationships
• Uncertainty Handling: Apply Dempster-Shafer theory to manage uncertainty and imprecision in evaluations
• Validation: Verify method correctness and effectiveness on actual refinery data

Advantages: This approach addresses limitations of entropy-based weighting methods and reduces total computation requirements while improving decision reliability [6].

Visualization Framework

Fuzzy MCDM Workflow for Refining Applications

Refining Application Decision Hierarchy

Research Reagent Solutions

Table 3: Essential Methodological Components for Fuzzy MCDM in Refining

Component	Function	Implementation Example
Fuzzy Set Extensions	Represent uncertain, vague information	Disc Spherical Fuzzy Sets (D-SFS) for crude oil pretreatment [2]
Weighting Methods	Determine relative importance of criteria	Rankability-based weighting to overcome decision contradictions [6]
Aggregation Operators	Combine multiple expert opinions	Aczel-Alsina based aggregation operators in D-SF framework [2]
MCDM Algorithms	Rank alternatives based on multiple criteria	Fuzzy TOPSIS for demulsifier selection [3]
Risk Assessment Frameworks	Model process operation risks	Fuzzy Risk-Based Maintenance (RBM) for asset failure prioritization [5]
Sensitivity Analysis Tools	Validate model robustness under varying conditions	Parameter variation and weight stability testing [7]

Fuzzy multi-criteria decision-making methodologies provide refined mathematical frameworks for addressing the complex optimization challenges inherent in oil refining operations. The application notes and experimental protocols detailed in this document establish comprehensive guidelines for implementing these advanced decision-support techniques across various refining contexts, from crude oil pretreatment to stabilization column control and demulsifier selection. By systematically incorporating expert knowledge with mathematical modeling while preserving the integrity of fuzzy information throughout the decision process, these approaches enable researchers and refinery professionals to achieve significant improvements in operational efficiency, cost reduction, and environmental compliance. The continued development and application of fuzzy MCDM frameworks represents a critical advancement path for addressing the increasingly complex challenges facing modern refining operations.

The Role of Fuzzy Set Theory in Managing Operational Uncertainty and Vague Data

Operational management in complex industrial processes like oil refining is fundamentally challenged by inherent uncertainties and vague data. Traditional deterministic models often fall short when dealing with imprecise measurements, subjective expert judgments, and fluctuating process parameters. Fuzzy set theory, introduced by Zadeh, provides a mathematical framework to represent and manage this vagueness by allowing partial set membership, defined by membership functions ranging between 0 and 1 [8] [9]. This capability is particularly valuable for oil-refining unit control, where multiple conflicting criteria—such as efficiency, cost, environmental impact, and safety—must be balanced simultaneously under uncertain conditions [1] [10]. The integration of fuzzy multi-criteria decision-making (MCDM) enables researchers and engineers to develop robust optimization and control strategies that closely mirror human reasoning and operational reality.

Application Notes: Fuzzy Systems in Oil Refining Operations

The following applications demonstrate the practical implementation of fuzzy set theory in managing operational uncertainty within oil refining contexts.

Risk-Based Maintenance (RBM) for Asset Failure Prevention

Objective: To prioritize maintenance activities by assessing the risk of asset failures, accounting for uncertainty in failure frequency and consequence data.

Implementation: A Fuzzy Logic System (FLS) using the Mamdani algorithm was developed to model risk, combining fuzzy estimates of failure likelihood with consequences related to safety, environment, operation downtime, and repair costs [5]. This approach directly addresses the engineering problem of uncertainty due to information lack in complex refinery risk modeling.

Key Outcomes: A case study at the Abadan oil refinery identified 26 asset failures. The fuzzy risk results showed that:

• 3 failures were at a semi-critical level
• 23 failures were non-critical The unit with a unified risk number less than 40 was in non-critical condition. Compared to traditional RBM, the fuzzy results demonstrated a better fit to operational data, providing a more accurate foundation for risk management planning and maintenance prioritization [5].

Multi-Criteria Optimization of Stabilization Column Operations

Objective: To optimize the operating modes of a primary oil-refining stabilization column under multiple conflicting criteria and fuzzy information.

Implementation: Researchers developed heuristic fuzzy MCDM methods based on modifying and combining different optimality principles. This approach utilized system models alongside the knowledge and experience of decision-makers, allowing for iterative improvement of decisions [1] [11]. The method operates directly on fuzzy information without converting it to equivalent crisp problems, thereby preserving the original fuzzy data and enhancing solution adequacy [1].

Key Outcomes: The proposed method successfully solved a two-criterion optimization problem for stabilization column parameters in a fuzzy environment. Results confirmed advantages over known methods by maximizing the use of collected fuzzy information and enabling more adequate decisions that reflect the complex, non-formalizable influences on column operation [1].

Criticality Analysis Using Picture Fuzzy Inference Systems

Objective: To determine the criticality of refinery assets for Reliability Centered Maintenance (RCM) under conditions of quantitative data scarcity.

Implementation: A novel Picture Fuzzy Inference System (PFIS) utilizing the Mamdani approach was developed. Picture Fuzzy Sets incorporate an additional dimension of hesitancy degree, alongside membership and non-membership functions, providing a more nuanced representation of uncertainty when processing verbal expressions from experts [8].

Key Outcomes: When applied to a crude distillation unit and compared with traditional matrix methods, the PFIS demonstrated effectiveness in refining the criticality determination process and maintenance prioritization. This approach proved particularly valuable in addressing uncertainties and hesitations resulting from inadequate assessments by decision-makers [8].

Demulsifier Selection Using Fuzzy TOPSIS

Objective: To systematically select optimal demulsifiers for crude oil dehydration by balancing multiple conflicting criteria under uncertainty.

Implementation: The Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS) was applied to evaluate and rank demulsifiers. This MCDM method quantifies expert evaluations using fuzzy logic, assessing alternatives based on their relative closeness to an ideal solution while considering criteria such as separation efficiency, environmental impact, cost-effectiveness, and ease of application [3].

Key Outcomes: Evaluation of four commercial demulsifiers identified Nalco Champion EC7135A as the top-ranked option with a closeness coefficient of 0.751, followed by Alcopol 500 (0.708), Polymer-based Demulsifier (0.692), and Schlumberger's ClearPhase (0.619). The study demonstrated that Fuzzy TOPSIS provides a structured, quantitative, and transparent approach superior to conventional trial-and-error or single-criterion assessments [3].

Table 1: Quantitative Comparison of Fuzzy Methods in Oil Refining Applications

Application Area	Fuzzy Method	Key Performance Metrics	Results
Risk-Based Maintenance	Mamdani Fuzzy Logic System	Unified risk number; Criticality classification	3 semi-critical, 23 non-critical failures identified; Better fit to data than traditional RBM [5]
Stabilization Column Optimization	Heuristic Fuzzy MCDM	Criteria satisfaction; Decision adequacy	Effective two-criterion optimization; Superior to known methods [1]
Demulsifier Selection	Fuzzy TOPSIS	Closeness coefficient (0-1 scale)	Nalco Champion (0.751), Alcopol 500 (0.708), Polymer-based (0.692), ClearPhase (0.619) [3]
Pipeline Risk Assessment	Subtractive Clustering FIS	Training RMSE; Check RMSE; Correlation coefficient (R²)	Best-fit model selection; Handled uncertainty in real-world circumstances [9]

Experimental Protocols

Protocol: Developing a Fuzzy Inference System for Risk Assessment

This protocol outlines the methodology for implementing a Fuzzy Inference System (FIS) for risk assessment in refinery operations, based on established approaches [5] [8] [9].

Phase 1: System Definition and Data Collection

• Define Input and Output Variables: Identify relevant risk factors (e.g., failure frequency, safety impact, environmental impact, operational downtime) as inputs, and risk criticality level as output [5].
• Establish Membership Functions: For each variable, define fuzzy sets (e.g., Low, Medium, High) and corresponding membership functions. Gaussian functions are often preferred for natural representation: μ_Aᵢ(x) = exp(-(cᵢ - x)² / (2σᵢ²)) where cᵢ is the center and σᵢ is the width of the i-th fuzzy set Aᵢ [9].
• Collect Fuzzy Data: Utilize expert evaluation methods, such as the Delphi technique, to gather and formalize fuzzy information representing the knowledge, experience, and intuition of domain experts [5] [10].

Phase 2: FIS Construction and Implementation

• Develop Fuzzy Rule Base: Create IF-THEN rules incorporating expert knowledge (e.g., "IF failure frequency is High AND safety impact is High THEN risk is Critical") [8].
• Select FIS Type: Choose appropriate inference system (Mamdani or Sugeno). Mamdani type is typically used for risk assessment as it generates fuzzy outputs that can be aggregated and defuzzified [8].
• Implement Inference Engine: Apply fuzzy logic operations (fuzzification, inference, aggregation) to map inputs to outputs using the defined rule base.

Phase 3: Defuzzification and Validation

• Defuzzify Outputs: Convert fuzzy output sets to crisp values using appropriate methods (e.g., centroid, bisector).
• Validate Model: Compare fuzzy results with traditional methods and operational data. Calculate performance indices such as Root Mean Square Error (RMSE) and correlation coefficient (R²) [9].
• Implement Prioritization: Rank assets or processes based on obtained risk numbers for maintenance planning and decision-making [5].

Protocol: Fuzzy Multi-Criteria Decision Making for Process Optimization

This protocol details the application of fuzzy MCDM for optimizing operating modes in oil-refining units [1] [3].

Phase 1: Problem Formulation in Fuzzy Environment

• Define Decision Criteria: Identify multiple, often conflicting criteria (e.g., product quality, energy consumption, environmental impact, cost).
• Formulate Fuzzy Evaluation Matrix: Construct a matrix where elements represent the fuzzy performance ratings of alternatives against each criterion. Use linguistic variables (e.g., Poor, Fair, Good) converted to fuzzy numbers.
• Determine Fuzzy Weights: Assign weights to criteria using appropriate methods (e.g., expert judgment, entropy-based methods, rankability-based weighting) to reflect their relative importance [6].

Phase 2: Application of Fuzzy MCDM Method

• Select Appropriate MCDM Technique: Choose based on problem characteristics (e.g., Fuzzy TOPSIS for ranking alternatives, fuzzy compromise programming for conflicting criteria).
• Normalize Fuzzy Decision Matrix: Convert diverse criteria dimensions into dimensionless comparable units.
• Construct Weighted Normalized Matrix: Multiply normalized fuzzy ratings by fuzzy weights.
• Determine Fuzzy Ideal Solutions: Identify Fuzzy Positive Ideal Solution (FPIS) and Fuzzy Negative Ideal Solution (FNIS).
• Calculate Closeness Coefficients: For Fuzzy TOPSIS, compute the distance of each alternative from FPIS and FNIS, then calculate relative closeness to ideal solution: CCᵢ = dᵢ⁻ / (dᵢ⁺ + dᵢ⁻) where dᵢ⁺ and dᵢ⁻ are distances from FPIS and FNIS respectively [3].

Phase 3: Decision Implementation

• Rank Alternatives: Sort alternatives based on calculated closeness coefficients in descending order.
• Sensitivity Analysis: Test robustness of results by varying criteria weights and evaluating rank stability.
• Implement Optimal Decision: Apply the highest-ranked alternative to process control and monitor performance.

Visualization: Fuzzy Inference System Workflow

The following diagram illustrates the logical workflow and structure of a typical Fuzzy Inference System as applied in oil-refining operational management:

Fuzzy Inference System Workflow - This diagram illustrates the transformation of crisp input data into actionable decisions through fuzzification, inference, and defuzzification processes.

Table 2: Key Research Reagent Solutions for Fuzzy Systems Implementation

Tool/Resource	Function/Purpose	Application Context
Mamdani Fuzzy Inference	Generates fuzzy outputs requiring defuzzification; integrates expert knowledge through interpretable IF-THEN rules	Risk assessment, criticality analysis, complex system modeling where transparency is crucial [5] [8]
Picture Fuzzy Sets (PFS)	Extends traditional fuzzy sets with hesitancy degree; better captures uncertainty and expert hesitation in evaluations	Criticality assessment in RCM when decision-makers show significant indecision or data is qualitatively described [8]
Fuzzy TOPSIS	Ranks alternatives by proximity to ideal solution; handles uncertainty in multi-criteria evaluations with linguistic variables	Demulsifier selection, supplier evaluation, process parameter optimization with multiple conflicting criteria [3] [6]
Subtractive Clustering FIS	Automatically generates fuzzy rules from data; solves "curse of dimensionality" in systems with many input variables	Pipeline risk assessment, complex system modeling with limited expert knowledge for rule specification [9]
Gaussian Membership Functions	Represents natural, smooth transition between set membership; non-zero at all points for continuous coverage	Most natural phenomena modeling; risk assessment studies with uncertain and vague data [9]

Fuzzy set theory provides an essential mathematical framework for managing operational uncertainty and vague data in oil-refining operations. Through various implementations—including fuzzy risk modeling, multi-criteria decision-making, and picture fuzzy inference systems—this approach enables more adequate and robust decision-making under conditions of information deficiency and ambiguity. The experimental protocols and visualization provided herein offer researchers and engineers practical methodologies for implementing these techniques in real-world refining contexts. As oil refining processes grow increasingly complex and environmental standards tighten, the application of fuzzy set theory in operational management will continue to provide critical support for optimizing performance while managing uncertainty.

Oil-refining operations are characterized by complex, interconnected processes where effective control and optimization are paramount for economic viability, safety, and product quality. However, these tasks are significantly complicated by pervasive uncertainties that impact decision-making at every level. This document, framed within broader research on fuzzy multi-criteria decision-making (FMCDM), identifies the key sources of this uncertainty and provides structured protocols for its analysis and mitigation. Traditional crisp optimization methods often fail when confronted with the fuzzy, incomplete, or non-formalizable information typical of chemical-technological systems (CTS) [1]. The FMCDM approach offers a robust framework for making adequate decisions by maximizing the use of collected fuzzy information, thus enhancing the adequacy of solutions developed for a fuzzy environment [1] [4].

Uncertainty in oil refining originates from multiple domains, including feedstock characteristics, market dynamics, operational processes, and the external environment. The table below categorizes and describes these primary sources.

Table 1: Key Sources of Uncertainty in Oil-Refining Unit Control and Optimization

Category	Specific Source	Description of Uncertainty	Impact on Refining Operations
Feedstock Quality	Variable Moisture Content	Fluctuations in water content of waste lubricant oil feedstocks [12].	Affects energy consumption, product quality (e.g., kinetic viscosity), and production cost [12].
Feedstock Quality	Variable Crude Oil Composition	Changes in the quality and composition of sourced crude oil [13].	Impacts crude ranking, processing yields, and necessitates frequent re-optimization of blending and processing.
Economic & Market	Crude Oil Price Volatility	Geopolitical events, supply decisions (e.g., OPEC+ announcements), and macroeconomic concerns cause price fluctuations [14].	Creates uncertainty in input costs, impacts refining margins, and affects strategic planning and profitability [15].
Economic & Market	Refining Margin Variability	Crack spreads for diesel and gasoline change based on seasonal demand, inventories, and international market pressures [14].	Directly affects profitability and dictates optimal product slate, requiring flexible operational strategies [16].
Economic & Market	Policy & Tariff Changes	Import tariffs (e.g., on steel) and evolving environmental regulations [16] [15].	Increases capital and operating costs (e.g., well costs, emissions costs) and can alter the competitive landscape [15].
Operational Process	Plant & Equipment Reliability	Unplanned outages, equipment failures, and suboptimal maintenance productivity [16].	Reduces availability, increases costs, and leads to failure to meet production targets.
Operational Process	Planning & Scheduling Inefficiency	Fragmented data, lack of clarity on risk authority, and inability to optimize end-to-end processes [13].	Leads to value leakage, with potential losses of \$0.50 to \$1.00 per barrel [13].
External Environment	Macro-Economic Shocks	Events like the COVID-19 pandemic, which caused massive demand shifts and price collapses [17].	Creates extreme market volatility, disrupts well-established price-quantity relationships, and amplifies other risks.
External Environment	Geopolitical Tensions	Attacks on energy infrastructure, trade disputes, and regional conflicts [14].	Threatens supply security, introduces volatility into commodity markets, and disrupts trade flows.

Experimental Protocols for Analyzing Uncertainty

To manage the uncertainties identified in Table 1, rigorous experimental and analytical protocols are required. The following sections detail methodologies for addressing feedstock, market, and operational uncertainties.

Protocol for Feedstock Uncertainty Analysis

This protocol assesses the impact of variable feedstock quality, such as moisture content in waste oil, on process economics and product quality using a sequential simulation and optimization approach [12].

1. Objective: To determine the optimal re-refining pathway for waste lubricant oil under uncertain moisture content, evaluating performance in economic, environmental, and product quality domains [12].

2. Experimental Workflow:

The following diagram outlines the sequential methodology for feedstock uncertainty analysis.

3. Materials and Reagents: Table 2: Research Reagent Solutions for Feedstock Uncertainty Analysis

Item	Function / Description
Aspen HYSYS Simulation Software	Process simulation environment to model re-refining pathways using custom fluid assays to mimic waste lubricant oil properties [12].
Peng Robinson Fluid Package	Thermodynamic model selected for its compatibility with hydrocarbon components in the re-refining process [12].
Waste Lubricant Oil Assay	Custom-defined fluid in HYSYS based on literature data (e.g., TBP curve, composition) to represent the feedstock [12].
Monte Carlo Simulation Engine	Mathematical technique (e.g., in Python, MATLAB, or specialized software) to perform stochastic sampling and predict outcome distributions [12].

4. Procedure:

• Superstructure Definition: Mathematically define all possible pre-treatment, treatment, and post-treatment pathways using material flow equations (Eqs. 1-6 in [12]).
• HYSYS Model Development: Develop rigorous process models in Aspen HYSYS for each pathway in the superstructure.
  • Use the custom fluid assay to define the waste oil feedstock.
  • Vary the moisture content by adjusting the water flowrate in the feed stream.
  • For each moisture level, run the simulation to convergence and record key output parameters: energy consumption, carbon emissions, and final product kinetic viscosity [12].
• Correlation Development: Using Design of Experiment (DOE) methodologies, analyze the data from step 2 to generate correlation functions that describe the relationship between moisture content and each key performance indicator [12].
• Monte Carlo Simulation: Define a probability distribution for the moisture content of the incoming waste oil. Using the correlation functions from step 3, run a Monte Carlo simulation (typically thousands of iterations) to compute the probability distributions for the economic, environmental, and quality outcomes for each pathway [12].
• Multi-Criteria Optimization: Evaluate the success probability of each pathway across the three domains. Employ a multi-criteria decision-making method, such as the weighted entropy sum technique, to identify the single optimal re-refining pathway that is most robust to the expected moisture content variation [12].

Protocol for Market Price Uncertainty Analysis

This protocol employs a semiparametric additive quantile regression to model the nonlinear and heterogeneous relationship between oil price uncertainty and financial performance, extending beyond traditional linear models [17].

1. Objective: To refine the evaluation of how oil price uncertainty, measured by the Crude Oil Volatility Index (OVX), impacts stock returns or refining margins, capturing asymmetric and nonlinear effects under different market conditions [17].

2. Methodology Details:

• Data Collection: Collect time-series data for the dependent variable (e.g., stock returns of a refining company) and independent variables (OVX, positive OVX shocks, negative OVX shocks, and control variables) over an extended period that includes major economic disruptions (e.g., the COVID-19 pandemic) [17].
• Model Specification: Apply a semiparametric additive quantile regression model. Unlike linear quantile regression, this model does not impose a strict parametric form on the relationship between OVX shocks and returns. Instead, it allows the data to determine the shape of this relationship through nonparametric functions, providing a more accurate and flexible assessment [17].
• Analysis: Execute the model across different quantiles (e.g., 0.05, 0.25, 0.5, 0.75, 0.95) to investigate impacts in bearish, normal, and bullish markets. The analysis will reveal dynamic, heterogeneous effects, such as the "U-shaped" impact of positive OVX shocks on returns in a bearish market [17].

Protocol for Operational Uncertainty & Value Chain Optimization

This protocol outlines a transformation approach to address operational inefficiencies and siloed decision-making that cause value leakage in refinery value chains.

1. Objective: To improve refining margins by \$0.50 to \$3.00 per barrel through a holistic Value Chain Optimization (VCO) transformation that addresses process, tool, and talent gaps [13] [16].

2. Methodology Details:

• Performance Baseline & Diagnosis: Establish current performance baselines for key metrics (e.g., planning vs. actual margin). Diagnose root causes of value leakage, such as fragmented economic data, infrequent plan updates, lack of cross-functional backcasting, and misaligned organizational incentives [13].
• Process Redesign & Tool Implementation:
  • Implement Robust Backcasting: Regularly compare actual performance to the best possible performance under the same conditions to identify and close value gaps [13].
  • Adopt Optimization-Based Scheduling: Replace or supplement simulation-based scheduling tools with optimization-based systems that can generate executable schedules meeting business goals, moving operations closer to the true operating line of the plant [18].
  • Leverage Digital & AI Tools: Deploy advanced analytics and AI across planning, scheduling, and asset management. For example, AI can optimize furnace operations and fuel gas systems, potentially saving \$0.30 to \$0.90 per barrel [16].
• Talent & Operating Model: Create cross-functional teams with end-to-end accountability. Institute rotational programs for early-tenure engineers across commercial, refining, and technical roles to build a deep pool of VCO talent [13].

Integrated Fuzzy Multi-Criteria Decision-Making Framework

The protocols in Section 3 generate complex, often conflicting, performance data across multiple domains (economic, environmental, quality). A Fuzzy Multi-Criteria Decision-Making (FMCDM) framework is essential to synthesize this information and identify the most robust and optimal solution.

1. Problem Formulation: The optimization and control of refining units are formally posed as a fuzzy multi-criteria problem without converting it first into a set of crisp problems. This approach prevents the loss of original fuzzy information, leading to more adequate solutions [1].

2. Heuristic FMCDM Method: The proposed framework utilizes heuristic methods based on the modification and combination of different principles of optimality, such as the main criterion and maximin [1] [4].

• Inputs: The framework incorporates system models (e.g., from Aspen HYSYS), knowledge, and the experience of the Decision Maker (DM).
• Process: It allows for the iterative improvement of decisions by evaluating alternatives against fuzzy criteria and constraints.
• Advantage: This method maximizes the use of collected fuzzy information, making it particularly effective for controlling complex production facilities characterized by non-formalizable parameters and expert knowledge [1].

The following diagram visualizes this integrated FMCDM workflow for refinery optimization.

3. Application Example: In a two-criterion optimization of stabilization column parameters (e.g., balancing energy consumption versus product quality), the FMCDM method has been shown to outperform known methods, confirming its advantages for decision-making in a fuzzy environment [1] [4].

Uncertainty in oil-refining unit control is an inherent and multi-faceted challenge, stemming from feedstock properties, market dynamics, and operational processes. Successfully navigating this complex landscape requires a move beyond traditional, crisp optimization methods. The experimental protocols outlined for feedstock, market, and operational analysis provide a structured approach to quantify these uncertainties. Ultimately, integrating the results from these protocols into a Fuzzy Multi-Criteria Decision-Making (FMCDM) framework offers a robust and mathematically sound methodology for identifying optimal and robust operating strategies, thereby enhancing refinery profitability, sustainability, and resilience in an increasingly volatile global market.

Multi-criteria decision-making (MCDM) represents a fundamental approach for evaluating and selecting alternatives based on multiple, often conflicting criteria. In complex industrial environments like oil refining, decision-makers face inherent uncertainties, vague information, and qualitative judgments that complicate traditional crisp evaluation methods. Fuzzy set theory, introduced by Zadeh, revolutionized this field by enabling mathematical representation and processing of this uncertain information [19] [20]. The progression from ordinary fuzzy sets to advanced spherical fuzzy sets has significantly enhanced our capacity to model real-world decision environments with greater accuracy and flexibility.

The oil refining industry presents particularly challenging environments for decision-making due to complex chemical-technological systems (CTS) characterized by a large number of interconnected technological units with parameters that are often non-formalizable and fuzzy [1] [21]. For instance, in primary oil-refining units, stabilization columns, fluid catalytic cracking units (FCCU), and delayed coking units (DCU), the influence of various parameters on operating modes and product quality often defies precise measurement and formalization [1] [22] [21]. This context has driven the development and application of increasingly sophisticated fuzzy MCDM frameworks that can accommodate these challenges while providing actionable insights for operational optimization.

Evolution of Fuzzy Set Extensions for MCDM

From Ordinary Fuzzy Sets to Spherical Fuzzy Sets

The evolution of fuzzy set extensions has progressively expanded our ability to handle uncertainty in decision-making processes:

• Fuzzy Sets (FS): The original concept introduced by Zadeh assigned a membership degree (MD) ∈ [0,1] to indicate how closely an element belongs to a set [19] [20].
• Intuitionistic Fuzzy Sets (IFS): Developed by Atanassov, IFS introduced non-membership degrees (¬MD) alongside membership degrees, with the constraint that MD + ¬MD ≤ 1 [19] [20].
• Pythagorean Fuzzy Sets (PyFS): Yager proposed PyFS to overcome IFS limitations, requiring that MD² + ¬MD² ≤ 1 [19].
• Picture Fuzzy Sets (PFS): Cuong and Kreinovich introduced positive, neutral, and negative membership degrees with MD + NMD + ¬MD ≤ 1, where NMD represents neutral membership degree [19].
• Spherical Fuzzy Sets (SFS): Mahmood et al. and Gündoğdu and Kahraman independently developed SFS, imposing the constraint MD² + NMD² + ¬MD² ≤ 1, providing greater flexibility in uncertainty management [19] [20].
• T-Spherical Fuzzy Sets (T-SFS): Extending SFS with (MD)ⁿ + (NMD)ⁿ + (¬MD)ⁿ ≤ 1 for integer n ≥ 2, offering even more flexibility in assigning membership values [19].
• pqr-Spherical Fuzzy Sets (pqr-SFS): The most flexible extension allowing different parameters for each dimension with (MD)^p + (NMD)^q + (¬MD)^r ≤ 1, where p, q, r are positive integers [19].

Table 1: Comparison of Fuzzy Set Extensions for MCDM

Fuzzy Set Type	Key Parameters	Constraints	Decision-Making Flexibility
Fuzzy Sets (FS)	Membership (μ)	0 ≤ μ ≤ 1	Basic
Intuitionistic FS (IFS)	μ, ν	μ + ν ≤ 1	Moderate
Pythagorean FS (PyFS)	μ, ν	μ² + ν² ≤ 1	High
Picture FS (PFS)	μ, η, ν	μ + η + ν ≤ 1	High
Spherical FS (SFS)	μ, η, ν	μ² + η² + ν² ≤ 1	Very High
T-Spherical FS (T-SFS)	μ, η, ν	(μ)ⁿ + (η)ⁿ + (ν)ⁿ ≤ 1	Very High
pqr-Spherical FS	μ, η, ν	(μ)^p + (η)^q + (ν)^r ≤ 1	Maximum

Key Advantages of Spherical Fuzzy Sets

Spherical fuzzy sets provide significant advantages for complex decision-making in oil refining contexts. The presence of three defined degrees (membership, non-membership, and hesitancy) allows decision-makers to express judgments more accurately than previous fuzzy set extensions [20]. The spherical structure provides a larger domain for assigning preferences, which is particularly valuable when dealing with expert knowledge that inherently contains hesitation and uncertainty [19] [20]. Furthermore, the squared normalization constraint (MD² + NMD² + ¬MD² ≤ 1) offers a more flexible framework for handling extreme cases that violate the linear constraints of picture fuzzy sets [19].

For oil refining applications, where operational data often combines precise measurements with expert qualitative assessments, spherical fuzzy sets enable more nuanced representation of this hybrid information. This capability has proven valuable in applications ranging from demulsifier selection to controlling operating modes of stabilization columns and delayed coking units [1] [3] [21].

Fuzzy MCDM Frameworks and Methodologies

Fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution)

The Fuzzy TOPSIS method extends the classical TOPSIS approach by incorporating fuzzy logic to handle uncertainty and vagueness in subjective judgments [3] [23]. This method evaluates alternatives based on their relative closeness to a fuzzy positive ideal solution (FPIS) and distance from a fuzzy negative ideal solution (FNIS). The fundamental principle involves selecting the alternative that simultaneously minimizes distance from the ideal solution while maximizing distance from the negative-ideal solution [3].

In oil refining applications, Fuzzy TOPSIS has been successfully implemented for demulsifier selection in crude oil dehydration [3]. The method systematically ranks demulsifiers such as Alcopol 500, Polymer-based Demulsifier, Nalco Champion EC7135A, and Schlumberger's ClearPhase based on criteria including separation efficiency, environmental impact, cost-effectiveness, and ease of application [3]. Experimental results demonstrated that Nalco Champion EC7135A achieved the highest closeness coefficient (0.751), making it the optimal choice according to this methodology [3].

Fuzzy AHP (Analytic Hierarchy Process)

Fuzzy AHP combines the structured hierarchy of traditional AHP with fuzzy set theory to accommodate uncertainty in pairwise comparisons [23]. This approach is particularly valuable when decision-makers struggle to assign precise numerical values to comparison judgments. The method structures complex decision problems into hierarchies, then uses fuzzy pairwise comparison matrices to derive weights for criteria and subcriteria [23].

In web-based Fuzzy Multi-Criteria Group Decision Making (FMCGDM) frameworks, Fuzzy AHP serves as the weighting engine to determine the relative importance of various criteria based on expert judgments [23]. This methodology has been applied to problems ranging from landfill site selection to optimization of oil refining operations [23].

Spherical Fuzzy Best-Worst Method (SF-BWM)

The Spherical Fuzzy Best-Worst Method represents a recent advancement that combines the efficiency of BWM with the expressive power of spherical fuzzy sets [20]. Compared to traditional BWM and fuzzy BWM, the SF-BWM requires fewer pairwise comparisons while providing a better consistency ratio [20]. Research has demonstrated that the consistency ratio obtained for SF-BWM is threefold better than traditional BWM and fuzzy BWM methods, leading to more accurate and reliable results [20].

The SF-BWM uses an optimization model based on nonlinear constraints to determine optimal spherical fuzzy weight coefficients [20]. This approach allows decision-makers to express judgment hesitancy separately from non-membership and membership degrees, providing a more nuanced representation of expert preferences in oil refining applications [20].

Complex Picture Fuzzy TOPSIS

For highly complex decision environments involving cyclic patterns and periodic uncertainties, Complex Picture Fuzzy Sets (CPFS) integrated with TOPSIS offer enhanced capabilities [24]. This approach incorporates both real and imaginary components in membership, abstinence, and non-membership degrees, enabling representation of cyclical uncertainties present in speech matching and sports training feature recognition [24]. While this advanced methodology shows promise for dynamic industrial processes with periodic behaviors, its application in oil refining represents an emerging research frontier.

Table 2: Comparison of Fuzzy MCDM Methods for Oil Refining Applications

Method	Key Features	Strengths	Oil Refining Applications
Fuzzy TOPSIS	Distance-based approach using fuzzy positive/negative ideal solutions	Handles subjective judgments well; intuitive methodology	Demulsifier selection [3]; Operational parameter optimization
Fuzzy AHP	Hierarchical structuring with fuzzy pairwise comparisons	Comprehensive criteria structuring; established methodology	System modeling; Criteria weighting in group decisions [23]
SF-BWM	Combines Best-Worst Method with spherical fuzzy sets	High consistency ratio; fewer pairwise comparisons needed	Determining criteria weights under high uncertainty [20]
Superiority & Inferiority Ranking	Uses T-spherical fuzzy sets for industry selection	Provides two complete rankings; handles high hesitation	Industrial growth optimization [25]
Fuzzy Multi-Criteria Optimization	Heuristic methods combining optimality principles	Effective for control and optimization in fuzzy environment	Stabilization column control [1]; DCU optimization [21]

Application Notes: Fuzzy MCDM for Oil Refining Unit Control

Case Study: Controlling Operating Modes of Stabilization Columns

In primary oil-refining units, stabilization columns present challenging control problems due to fuzzy initial information and complex dynamics. Orazbayev et al. developed heuristic fuzzy multi-criteria decision-making methods for optimizing and controlling operating modes of these systems [1]. Their approach combined formal methods (experimental-statistical) with informal methods (expert evaluations, fuzzy set theory) to develop statistical and fuzzy models of the stabilization column [1].

The implementation followed a structured protocol:

• System Analysis: Identification of key input parameters (feed composition, flow rates, temperature, pressure) and output variables (product quality, efficiency metrics)
• Model Development: Creation of hybrid statistical-fuzzy models based on experimental data and expert knowledge
• Criteria Definition: Establishment of multiple, often conflicting optimization criteria (energy efficiency, product quality, operational stability)
• Fuzzy Optimization: Application of heuristic methods combining different optimality principles (main criterion and maximin) for two-criterion optimization
• Validation: Performance comparison against conventional control methods demonstrating advantages in handling fuzzy information [1]

This approach successfully addressed the challenge of inadequate crisp data by maximizing the use of collected fuzzy information, leading to more adequate decisions in the fuzzy environment of stabilization column operation [1].

Case Study: Fluid Catalytic Cracking Unit (FCCU) Control

Fluid Catalytic Cracking Units represent complex systems with significant interactions between variables including gas oil supply temperature (Tf), gas oil supply flow rate (Ff), and air temperature (Ta). Research has demonstrated the superiority of fuzzy logic controllers over conventional PI controllers for managing riser and regenerator temperatures (TR, TG) in industrial Universal Oil Products (UOP) FCCUs [22].

The experimental protocol implemented:

• System Modeling: MATLAB simulation based on mass and energy balance principles of the FCCU
• Controller Design: Implementation of a fuzzy logic controller with five fuzzy sets generating 25 rules
• Performance Evaluation: Introduction of disturbances in gas oil supply temperature, flow rate, and air temperature
• Comparative Analysis: Evaluation of PI and fuzzy controllers based on integral absolute error, response stability, and settling times

Results demonstrated that the fuzzy logic controller outperformed the PI controller, exhibiting lower integral absolute error, more stable responses, and shorter settling times [22]. This performance advantage highlights the value of fuzzy-based control approaches for complex, interacting systems prevalent in oil refining.

Case Study: Delayed Coking Unit (DCU) Optimization

Delayed Coking Units operate under significant uncertainty due to the fuzzy nature of available information. A system of models for simulation and optimization of DCU operating modes in a fuzzy environment was developed combining experimental-statistical data with expert knowledge [21]. This approach recognized that many real CTS in practice operate under uncertainty associated with the fuzzy nature of available information, complicating model development and optimization [21].

The methodology involved:

• System Synthesis: Development of mathematical models of interconnected DCU units combined into a unified system
• Hybrid Modeling: Combination of formal (experimental-statistical) and informal methods (expert evaluations, fuzzy set theory)
• Integrated Optimization: Determination of optimal input and operational parameters maximizing coke production with specified quality indicators
• Knowledge Integration: Incorporation of decision-maker experience, knowledge, and intuition through fuzzy modeling approaches

This systematic approach to developing a model network for fuzzy-described CTS enabled more adequate modeling and optimization of DCU operating modes compared to conventional crisp optimization methods [21].

Experimental Protocols and Methodologies

Protocol 1: Fuzzy TOPSIS for Demulsifier Selection

Purpose: To systematically evaluate and rank demulsifiers for crude oil dehydration using Fuzzy TOPSIS methodology [3].

Materials: Candidate demulsifiers (e.g., Alcopol 500, Polymer-based Demulsifier, Nalco Champion EC7135A, Schlumberger's ClearPhase); Evaluation criteria weights; Expert evaluation team.

Procedure:

• Criteria Definition: Establish evaluation criteria (separation efficiency, environmental impact, cost-effectiveness, ease of application)
• Weight Assignment: Determine fuzzy weights for each criterion using expert judgments
• Decision Matrix: Construct fuzzy decision matrix incorporating expert evaluations of each demulsifier against all criteria
• Normalization: Normalize the fuzzy decision matrix to ensure comparability across criteria
• Weighted Matrix: Construct weighted normalized fuzzy decision matrix
• Ideal Solutions: Determine fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS)
• Distance Calculation: Calculate distances of each alternative from FPIS and FNIS
• Closeness Coefficients: Compute closeness coefficient for each demulsifier
• Ranking: Rank demulsifiers based on descending order of closeness coefficients

Validation: Compare results with conventional selection methods; Verify operational performance of top-ranked demulsifier.

Protocol 2: Spherical Fuzzy BWM Implementation

Purpose: To determine optimal criteria weights using spherical fuzzy sets with enhanced consistency ratio [20].

Materials: Decision criteria set; Expert decision-makers; Computational tools for solving optimization models.

Procedure:

• Criteria Determination: Identify the set of decision criteria {c1, c2, ..., cn}
• Best-Worst Identification: Determine the most important (best) and least important (worst) criteria
• Spherical Fuzzy Comparisons: Conduct spherical fuzzy pairwise comparisons between:
  • Best criterion and all other criteria
  • All criteria and the worst criterion
• Optimization Model: Formulate and solve nonlinear optimization model to determine spherical fuzzy weight coefficients
• Consistency Verification: Calculate consistency ratio using proposed validation methodology
• Weight Extraction: Derive final criteria weights from spherical fuzzy weight coefficients

Validation: Compare consistency ratios with traditional BWM and fuzzy BWM; Verify results through sensitivity analysis.

Protocol 3: Fuzzy Control System Design for Process Units

Purpose: To design and implement fuzzy logic controllers for complex process units like FCCUs [22].

Materials: Process models (first-principles or empirical); Historical operational data; Fuzzy logic development environment.

Procedure:

• Variable Identification: Identify controlled variables (e.g., riser temperature, regenerator temperature) and manipulated variables (e.g., flow rates, temperatures)
• Fuzzification: Define fuzzy sets and membership functions for input and output variables
• Rule Development: Create fuzzy rule base (e.g., 25 rules from 5 fuzzy sets)
• Inference Engine: Implement fuzzy inference mechanism (typically Mamdani-type)
• Defuzzification: Select and implement appropriate defuzzification method
• Simulation: Program implementation using appropriate simulation tools (e.g., MATLAB)
• Performance Testing: Introduce disturbances to evaluate controller performance
• Comparative Analysis: Compare with conventional controllers (e.g., PI) using metrics like integral absolute error, settling time, and response stability

Validation: Conduct closed-loop tests; Verify robustness under varying operating conditions.

Visualization of Fuzzy MCDM Framework

The following diagram illustrates the integrated workflow for implementing fuzzy MCDM in oil refining applications:

Fuzzy MCDM Implementation Workflow illustrates the systematic process for applying fuzzy MCDM frameworks to oil refining decision problems, showing key stages from problem definition through implementation.

Table 3: Essential Research Reagents and Computational Tools for Fuzzy MCDM

Tool/Resource	Type	Function/Purpose	Application Context
MATLAB Fuzzy Logic Toolbox	Software	Implementation of fuzzy inference systems and controllers	FCCU control system design [22]; Stabilization column optimization
- R, Python (scikit-fuzzy, PyFuzzy)	Programming Libraries	Custom fuzzy system development and algorithm implementation	Experimental fuzzy MCDM method development
- Linguistic Scale Converters	Methodological Tool	Transformation between linguistic assessments and fuzzy numbers	Expert judgment quantification in spherical fuzzy BWM [20]
- Consistency Ratio Calculators	Validation Tool	Assessment of pairwise comparison consistency in AHP/BWM	SF-BWM validation [20]
- Distance Measure Algorithms	Computational Tool	Calculation of Euclidean and other distances in fuzzy TOPSIS	Alternative ranking in demulsifier selection [3]
- Aggregation Operators	Mathematical Tool	Combination of multiple expert opinions into collective judgment	Group decision-making in waste location selection [23]
- Web-based FMCGDM Frameworks	Integrated Platform	Implementation of fuzzy Delphi, fuzzy AHP, and fuzzy TOPSIS	Multi-expert decision problems with geographical distribution [23]

Fuzzy MCDM frameworks have evolved significantly from basic fuzzy TOPSIS to advanced spherical fuzzy sets, providing increasingly sophisticated tools for handling the complex uncertainties inherent in oil refining operations. The progression has enabled more accurate representation of expert knowledge, particularly regarding hesitation and uncertainty in judgments, leading to more reliable decision outcomes in applications ranging from demulsifier selection to control of complex process units.

Future research directions should focus on several emerging areas. First, the integration of machine learning with fuzzy MCDM approaches shows promise for enhancing predictive accuracy in decision models [3]. Second, the development of real-time fuzzy MCDM systems could enable dynamic optimization of refining operations in response to changing conditions. Third, further exploration of complex spherical fuzzy sets and their application to cyclical processes in refining could yield significant improvements. Finally, standardized frameworks for validating and comparing fuzzy MCDM methodologies would strengthen methodological rigor and promote wider adoption in industrial practice.

As oil refining faces increasing complexity and sustainability challenges, the continued advancement and application of fuzzy MCDM frameworks will play a crucial role in optimizing operations, reducing costs, and enhancing environmental performance. The protocols and application notes provided in this overview offer researchers and practitioners a foundation for implementing these powerful methodologies in their own operational contexts.

The Critical Need for Structured Decision-Making in Crude Oil Pretreatment and Process Control

The pretreatment of crude oil is a critical frontier in the oil and gas sector, where effective separation techniques directly determine operational efficiency, product quality, and environmental compliance. Industry data demonstrate that advanced pretreatment techniques can reduce water content by up to 95% and contaminants by up to 90%, significantly enhancing the quality of recovered crude oil while reducing energy consumption by 20% [2]. However, selecting optimal pretreatment strategies and chemicals involves balancing multiple, often conflicting criteria under significant uncertainty, creating a complex decision-making landscape for researchers and engineers.

Within this context, fuzzy multi-criteria decision-making (MCDM) approaches have emerged as powerful frameworks for handling the inherent vagueness and subjective judgments in crude oil pretreatment evaluations. These methods systematically quantify linguistic assessments and imprecise data, enabling more robust and transparent decision processes. This application note details protocols for implementing two prominent fuzzy MCDM methodologies—the D-SF-MEREC-SWARA-MARCOS framework and Fuzzy TOPSIS—within crude oil pretreatment and process control research.

Theoretical Frameworks and Aggregation Operators

Disc Spherical Fuzzy Sets with Aczel-Alsina Norms

The Disc Spherical Fuzzy Sets (D-SFSs) framework extends the established Spherical Fuzzy Set paradigm by incorporating circular components across three dimensions: membership, non-membership, and abstinence degrees. This provides a more flexible representation of uncertainty and expert hesitancy [2] [3]. When combined with Aczel-Alsina aggregation operators, which offer specific parameterized norms for operations, the D-SFS framework enables sophisticated handling of ambiguous evaluation data in crude oil pretreatment scenarios.

Table 1: Core Components of the D-SFS Framework for Crude Oil Pretreatment

Component	Mathematical Representation	Role in Decision-Making
Membership Degree	μ(x) ∈ [0,1]	Degree of agreement with a given criterion
Non-Membership Degree	ν(x) ∈ [0,1]	Degree of disagreement with a given criterion
Abstinence Degree	π(x) ∈ [0,1]	Degree of refusal to provide opinion
Radius Parameter	r ∈ [0,1]	Defines the disc radius for circular interpretation
Aczel-Alsina Norm	Varies with parameter ν	Controls aggregation behavior of fuzzy information

Fuzzy TOPSIS for Chemical Selection

The Fuzzy Technique for Order Preference by Similarity to Ideal Solution (Fuzzy TOPSIS) builds upon classical TOPSIS by incorporating fuzzy logic to handle uncertainty in criterion evaluations. This method evaluates alternatives based on their relative closeness to a fuzzy positive ideal solution while maximizing distance from the fuzzy negative ideal solution [3]. The approach is particularly valuable for demulsifier selection where subjective judgments and incomplete data complicate decision processes.

Protocol 1: Implementing D-SF-MEREC-SWARA-MARCOS for Pretreatment Technology Selection

Objective and Applications

This protocol provides a step-by-step methodology for implementing the integrated D-SF-MEREC-SWARA-MARCOS approach to select optimal crude oil pretreatment technologies. The hybrid method combines objective and subjective weighting procedures with an advanced ranking mechanism, making it suitable for complex decision environments with multiple experts and uncertain data [2].

Experimental Workflow

The following diagram illustrates the complete workflow for implementing the D-SF-MEREC-SWARA-MARCOS methodology:

Step-by-Step Procedure

Step 1: Problem Structuring and Criteria Definition

• Identify potential crude oil pretreatment alternatives (e.g., membrane filtration, electrostatic coalescers, chemical demulsifiers)
• Define evaluation criteria across technical, economic, and environmental dimensions
• Establish a panel of decision experts (typically 3-5 specialists with refinery operations experience)

Step 2: D-SF Evaluation Matrix Construction

• Each expert evaluates alternatives against criteria using D-SF linguistic terms
• Convert linguistic evaluations to D-SF numbers (μ, ν, π, r)
• Aggregate individual matrices using D-SF weighted averaging operators

Table 2: D-SF Linguistic Scale for Expert Evaluations

Linguistic Term	D-SF Number (μ, ν, π)	Radius (r)
Extremely High	(0.95, 0.10, 0.15)	0.1
Very High	(0.85, 0.20, 0.25)	0.1
High	(0.75, 0.30, 0.35)	0.1
Moderate	(0.50, 0.45, 0.50)	0.1
Low	(0.35, 0.60, 0.45)	0.1
Very Low	(0.25, 0.70, 0.40)	0.1
Extremely Low	(0.10, 0.85, 0.25)	0.1

Step 3: Objective Weight Calculation using MEREC

• Apply the Method based on the Removal Effects of Criteria (MEREC)
• Calculate overall performance of alternatives using logarithmic function
• Remove each criterion and recalculate performance to determine its impact
• Compute objective weights based on removal effects

Step 4: Subjective Weight Calculation using SWARA

• Implement Step-wise Weight Assessment Ratio Analysis (SWARA)
• Experts rank criteria in descending order of importance
• Assess comparative importance of successive criteria
• Compute subjective weights based on comparative importance ratings

Step 5: Integrated Weight Determination

• Combine objective and subjective weights using linear integration
• Apply integration formula: wj = α × wj(Objective) + (1-α) × w_j(Subjective)
• Where α represents the decision strategy coefficient (0≤α≤1)

Step 6: MARCOS Ranking with D-SF Information

• Determine D-SF ideal and anti-ideal solutions
• Construct extended initial decision matrix
• Normalize the extended matrix using appropriate normalization techniques
• Calculate utility functions for alternatives relative to ideal and anti-ideal solutions
• Rank pretreatment alternatives based on utility degrees

Data Collection and Analysis

For case study validation, collect the following quantitative data for each pretreatment alternative:

Table 3: Quantitative Data Requirements for Pretreatment Technology Evaluation

Criterion	Measurement Method	Units	Target Values
Separation Efficiency	Water content analysis pre/post treatment	% reduction	90-95%
Contaminant Removal	SARA analysis for asphaltene, resin, sediment content	% removal	85-90%
Energy Consumption	Direct energy input measurement	kWh/bbl	20% reduction baseline
Operational Cost	CAPEX/OPEX analysis	$/bbl	Case-specific
Environmental Impact	Carbon emissions, waste generation	tCO2e/bbl	Regulatory compliance
Scalability	Throughput flexibility assessment	% design capacity	70-130%

Protocol 2: Fuzzy TOPSIS for Demulsifier Selection

Objective and Applications

This protocol details the application of Fuzzy TOPSIS for selecting optimal demulsifiers in crude oil dehydration processes, systematically addressing the need to balance separation efficiency, environmental impact, cost-effectiveness, and operational feasibility [3].

Experimental Workflow

The following diagram illustrates the Fuzzy TOPSIS workflow for demulsifier evaluation:

Step-by-Step Procedure

Step 1: Criteria Definition and Demulsifier Selection

• Identify candidate demulsifiers (e.g., Alcopol 500, Polymer-based Demulsifier, Nalco Champion EC7135A, Schlumberger's ClearPhase)
• Define evaluation criteria:
  • Separation Efficiency: Bottle test method measuring water separation over time
  • Environmental Impact: Biodegradability, toxicity assessment
  • Cost-Effectiveness: $/bbl treatment cost
  • Ease of Application: Dosage requirements, mixing energy

Step 2: Fuzzy Decision Matrix Construction

• Convert performance ratings to triangular fuzzy numbers (l, m, u)
• Assign linguistic variables for criterion importance (Very Low to Very High)
• Construct m × n fuzzy decision matrix for m demulsifiers and n criteria

Step 3: Fuzzy Weight Assignment

• Determine fuzzy weights for each criterion using expert judgment
• Convert linguistic importance ratings to triangular fuzzy weights

Step 4: Construction of Weighted Fuzzy Matrix

• Multiply fuzzy decision matrix by fuzzy weights
• Preserve the triangular fuzzy number structure throughout operations

Step 5: Determination of Ideal Solutions

• Identify Fuzzy Positive Ideal Solution (FPIS) for benefit criteria
• Identify Fuzzy Negative Ideal Solution (FNIS) for cost criteria
• Account for the different natures of evaluation criteria

Step 6: Distance Calculation

• Calculate distance between each alternative and FPIS/FNIS
• Use vertex method for distance between triangular fuzzy numbers

Step 7: Closeness Coefficient Computation

• Compute closeness coefficient (CC) for each demulsifier
• Apply formula: CCi = di^- / (di^+ + di^-)
• Where di^+ is distance from FPIS and di^- is distance from FNIS

Step 8: Ranking and Selection

• Rank demulsifiers in descending order of closeness coefficient
• Select demulsifier with highest CC value as optimal choice

Data Collection and Laboratory Methods

Bottle Test Protocol for Separation Efficiency:

• Prepare crude oil emulsion samples with identical water content (typically 20-30%)
• Add predetermined demulsifier dosage (25-500 ppm range)
• Heat samples to designated temperature (typically 50-70°C)
• Monitor water separation at regular intervals (5, 10, 20, 30, 60, 120 minutes)
• Record percentage water separation versus time
• Calculate separation efficiency metrics

Environmental Impact Assessment:

• Conduct biodegradability tests per OECD guidelines
• Measure aquatic toxicity using Daphnia magna or similar bioindicators
• Assess bioaccumulation potential through octanol-water partition coefficients

The Scientist's Toolkit: Research Reagent Solutions

Table 4: Essential Research Reagents and Materials for Crude Oil Pretreatment Studies

Reagent/Material	Function	Application Notes
Commercial Demulsifiers (Alcopol 500, Nalco Champion EC7135A)	Break water-in-oil emulsions by disrupting interfacial films	Typical dosage 25-500 ppm; performance temperature dependent
Synthetic Brine Solutions	Simulate produced water chemistry for emulsion studies	Vary salinity (10,000-100,000 ppm) to match field conditions
Asphaltene/Resin Standards	Model oil components for studying stabilization mechanisms	Isolate from crude oil using standard precipitation methods
Membrane Filtration Modules	Physical separation of water and contaminants	Pore size 0.01-0.1 μm; assess fouling potential
Electrostatic Coalescer Units	Promote water droplet coalescence via electric fields	Optimize field strength (0.5-5 kV/cm) and frequency
Analytical Standards (n-alkanes, biomarkers)	Quantification and method validation	Use for GC-MS/SARA analysis calibration

Case Study Validation and Performance Metrics

D-SF-MEREC-SWARA-MARCOS Application

A recent case study applying the D-SF framework to crude oil pretreatment demonstrated the method's effectiveness in ranking alternative technologies. The integrated approach successfully handled conflicting criteria and expert disagreement, with validation through comparison with CoCoSo method confirming reliability [2]. The D-SF framework showed particular strength in managing the high uncertainty in environmental impact assessments and long-term performance predictions.

Fuzzy TOPSIS Validation

In demulsifier selection studies, Fuzzy TOPSIS application revealed Nalco Champion EC7135A as the top-ranked option with a closeness coefficient of 0.751, followed by Alcopol 500 (0.708), Polymer-based Demulsifier (0.692), and Schlumberger's ClearPhase (0.619) [3]. The method provided a structured, quantitative approach that outperformed conventional trial-and-error selection processes, reducing evaluation time by approximately 40% while improving dehydration efficiency by 15-20%.

The structured decision-making frameworks presented in this application note provide researchers and refinery professionals with robust methodologies for addressing complex choices in crude oil pretreatment. The D-SF-MEREC-SWARA-MARCOS approach offers particular advantages for technology selection problems with multiple experts and significant data uncertainty, while Fuzzy TOPSIS delivers efficient performance for chemical selection applications like demulsifier evaluation.

Successful implementation requires careful attention to criterion definition, appropriate linguistic scale selection, and validation through sensitivity analysis. Future research directions include integration with machine learning predictive models, real-time operational data incorporation, and expansion to emerging eco-friendly pretreatment technologies.

Core FMCDM Methodologies and Their Application in Refinery Operations

In-Depth Analysis of the Fuzzy TOPSIS Methodology for Demulsifier Selection

The effective separation of water from crude oil is essential for maintaining oil quality, optimizing production efficiency, and minimizing operational challenges in the petroleum industry [3]. However, selecting an optimal demulsifier remains a complex problem due to the need to balance separation efficiency, environmental impact, cost-effectiveness, and ease of application [3]. This study addresses this challenge by applying the Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS) method, a robust multi-criteria decision-making (MCDM) approach, to evaluate and rank demulsifiers under uncertain conditions systematically [3]. The results indicate that this methodology provides a structured, quantitative, and transparent approach to demulsifier selection, enabling more data-driven and sustainable selection processes while reducing operational costs and improving crude oil dehydration efficiency [3].

Crude oil production is inherently accompanied by forming water-in-oil (W/O) emulsions, a complex mixture in which fine water droplets are dispersed within the oil matrix [3]. These emulsions are stabilized by naturally occurring surfactants present in crude oil, such as asphaltenes, resins, waxes, and particulate matter [3]. These substances form interfacial films around water droplets, preventing their coalescence and making separation challenging [3].

The petroleum industry relies heavily on chemical demulsifiers, which are designed to break emulsions and facilitate the separation of water from oil, thereby mitigating these challenges [3]. Demulsifiers disrupt the stabilizing forces at the oil-water interface, promoting the coalescence of water droplets and allowing gravity or centrifugal separation to occur [3]. The importance of selecting an appropriate demulsifier cannot be overstated, as its effectiveness directly impacts water removal efficiency, oil recovery rates, and downstream process integrity [3].

Historically, demulsifier selection has been conducted through empirical approaches, such as laboratory bottle tests or field trials [3]. While these methods provide valuable data, they are often time-consuming and limited in scope [3]. Furthermore, traditional selection methods often focus on a single criterion, such as separation efficiency, while neglecting other critical factors, including cost, environmental impact, and ease of application [3]. This one-dimensional focus can result in suboptimal decisions that compromise long-term operational and sustainability goals [3].

Multi-criteria decision-making (MCDM) tools have gained traction in recent years to address these limitations [3]. Among these, the Fuzzy TOPSIS stands out as a robust framework for handling complex decision-making scenarios [3]. FTOPSIS builds on the classical TOPSIS method by incorporating fuzzy logic, quantifying, and including uncertainty and vagueness in criteria evaluations [3]. This is particularly valuable in demulsifier selection, where subjective judgments and incomplete data often play a role [3].

Theoretical Framework of Fuzzy TOPSIS

Fuzzy TOPSIS is a multi-criteria decision-making method that enhances the classical TOPSIS by incorporating fuzzy logic [3]. It is designed to handle uncertainty and vagueness, often present in decision-making scenarios involving subjective judgments [3]. When selecting the optimal demulsifier, Fuzzy TOPSIS helps compare alternatives based on multiple criteria and ranks them according to their proximity to an ideal solution [3].

The fundamental principle of TOPSIS is that the chosen alternative should have the shortest geometric distance from the positive ideal solution and the longest geometric distance from the negative ideal solution [3]. The fuzzy extension of this method incorporates triangular or trapezoidal fuzzy numbers to represent the uncertainty in decision-makers' judgments about the performance ratings of alternatives and the weights of criteria [3].

For problems involving multiple decision-makers, the technique can be extended to multi-criteria group decision-making (MCGDM), where the opinions of several experts are aggregated [26]. This approach uses pentagonal fuzzy numbers for the final ranking of alternatives, providing a more nuanced handling of uncertainty in group decision environments [26].

Application to Demulsifier Selection

Evaluation Criteria for Demulsifiers

The evaluation criteria for demulsifiers typically include four key dimensions [3]:

• Separation Efficiency: The effectiveness of the demulsifier in breaking emulsions and facilitating water separation.
• Environmental Impact: The ecological consequences and sustainability considerations of using the demulsifier.
• Cost Effectiveness: The economic feasibility considering both initial costs and operational expenses.
• Ease of Application: The practicality of implementation in existing operational systems.

Experimental Demulsifier Performance

In the referenced study, four commercial demulsifiers were evaluated using the Fuzzy TOPSIS methodology [3]. The quantitative results are summarized in the table below.

Table 1: Performance Evaluation of Commercial Demulsifiers Using Fuzzy TOPSIS

Demulsifier Name	Closeness Coefficient	Ranking
Nalco Champion EC7135A	0.751	1
Alcopol 500	0.708	2
Polymer-based Demulsifier	0.692	3
Schlumberger's ClearPhase	0.619	4

The closeness coefficient represents the relative closeness to the fuzzy positive ideal solution, with values ranging from 0 to 1 [3]. Higher values indicate better overall performance across all evaluation criteria [3]. Nalco Champion EC7135A achieved the highest closeness coefficient (0.751), making it the top-ranked demulsifier due to its superior separation efficiency and lower environmental impact [3].

Research Reagents and Materials

Table 2: Essential Research Reagents and Materials for Demulsifier Evaluation

Reagent/Material	Function/Application
Alcopol 500	Commercial demulsifier formulation for crude oil dehydration
Polymer-based Demulsifier	Chemical formulation utilizing polymeric structures for emulsion breaking
Nalco Champion EC7135A	High-performance demulsifier with superior separation characteristics
Schlumberger's ClearPhase	Commercial demulsifier solution for oil-water separation
Crude Oil Samples	Natural emulsions for testing demulsifier efficacy
Asphaltenes, Resins, Waxes	Naturally occurring surfactants that stabilize water-in-oil emulsions

Experimental Protocols and Methodologies

Fuzzy TOPSIS Implementation Protocol

Step 1: Define the Decision Matrix

• Identify alternatives (demulsifiers) and evaluation criteria
• Construct a decision matrix with alternatives as rows and criteria as columns
• Collect performance ratings for each alternative against each criterion

Step 2: Determine Criteria Weights

• Use expert evaluations to assign weights to each criterion
• Convert linguistic terms to fuzzy numbers to handle uncertainty
• Aggregate individual judgments if multiple experts are involved

Step 3: Construct the Fuzzy Decision Matrix

• Convert crisp values to fuzzy numbers using appropriate membership functions
• Normalize the fuzzy decision matrix to ensure comparability across criteria

Step 4: Calculate Weighted Fuzzy Decision Matrix

• Multiply the normalized fuzzy decision matrix by the fuzzy weight of each criterion

Step 5: Determine Fuzzy Positive and Negative Ideal Solutions

• Identify the fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS)
• FPIS represents the best performance values for each criterion
• FNIS represents the worst performance values for each criterion

Step 6: Calculate Separation Measures

• Compute the distance of each alternative from FPIS and FNIS
• Use appropriate distance measures for fuzzy numbers

Step 7: Calculate Closeness Coefficient

• Compute the relative closeness of each alternative to the ideal solution
• Rank alternatives based on closeness coefficient values

Demulsifier Performance Testing Protocol

Step 1: Sample Preparation

• Collect representative crude oil samples with natural emulsified water
• Ensure sample homogeneity before testing
• Maintain consistent temperature conditions throughout preparation

Step 2: Demulsifier Application

• Add predetermined dosage of demulsifier to crude oil samples
• Use consistent mixing procedures to ensure proper dispersion
• Maintain precise temperature control during application

Step 3: Separation Monitoring

• Monitor water separation over defined time intervals
• Record separated water volumes at regular intervals
• Document interface clarity and emulsion break characteristics

Step 4: Data Collection and Analysis

• Measure final water separation efficiency
• Assess oil quality parameters in dehydrated oil
• Evaluate processing characteristics and residual emulsion stability

Workflow Visualization

Integration with Oil-Refining Unit Control Research

The application of Fuzzy TOPSIS for demulsifier selection aligns with broader research initiatives in fuzzy multi-criteria decision-making for oil-refining unit control [1]. Technological processes of oil refining, petrochemistry, and other industries are characterized by complex interconnected units with many parameters, the influence of which on operating modes is often non-formalizable and characterized by fuzziness [1].

In the context of oil-refining operations, many complex production facilities are characterized by a lack and fuzziness of initial information [1]. Such objects, in the presence of experienced operators and experts, are effectively managed due to their experience, knowledge, and intuition [1]. However, many control criteria and restrictions are not clearly described in the natural language of domain experts [1]. Therefore, to solve the problems of controlling the operating modes of fuzzy complex objects, it is more appropriate to use fuzzy multi-criteria decision-making with the participation of decision-makers [1].

The stabilization column of primary oil-refining units represents a typical example where fuzzy MCDM methods can be effectively applied [1]. Using the proposed heuristic methods based on the main criterion and maximin approach, the problem of two-criterion optimization of stabilization column parameters in a fuzzy environment can be successfully solved [1]. The results obtained confirm the advantages of proposed fuzzy decision-making methods compared to results from known methods [1].

The Fuzzy TOPSIS methodology provides a structured, quantitative, and transparent approach to demulsifier selection in crude oil dehydration processes [3]. By systematically evaluating multiple criteria, including separation efficiency, environmental impact, cost-effectiveness, and ease of application, this approach enables more informed and sustainable decision-making in petroleum industry operations [3].

The application of this methodology to evaluate four commercial demulsifiers demonstrated its practical utility, with Nalco Champion EC7135A emerging as the optimal choice due to its superior separation efficiency and lower environmental impact [3]. This approach represents a significant advancement over traditional trial-and-error or single-criterion assessment methods, offering a more robust framework for decision-making under uncertainty [3].

Future research should focus on incorporating real-time operational data, expanding the evaluation to emerging eco-friendly demulsifiers, and integrating predictive machine learning models to enhance the accuracy of the selection process [3]. Furthermore, the integration of fuzzy MCDM approaches with broader oil-refining unit control systems represents a promising direction for comprehensive optimization of petroleum production processes [1].

Application of Disc Spherical Fuzzy Sets (D-SFSs) with Aczel-Alsina Aggregation for Crude Oil Pretreatment

In the oil and gas sector, effective crude oil pretreatment is a critical frontier for maximizing the efficiency of extraction and refining operations. The integration of advanced pretreatment techniques has been shown to improve separation efficiency significantly, reducing water content by 95% and contaminants by up to 90%, while also achieving a 20% reduction in overall energy requirements [27]. However, the selection of an optimal pretreatment strategy is inherently complex, characterized by multiple conflicting criteria, uncertain operational data, and the need to incorporate expert judgments that are often vague or imprecise.

To address these challenges within the broader thesis context of fuzzy multi-criteria decision-making (MCDM) for oil-refining unit control, this paper introduces a novel application of Disc Spherical Fuzzy Sets (D-SFSs) integrated with Aczel-Alsina aggregation operators [27] [28]. D-SFSs provide a robust framework for handling the ambiguity and uncertainty in expert evaluations by incorporating membership, non-membership, and hesitancy degrees defined within a circular domain, offering a larger space for the depiction of uncertain information than picture fuzzy sets or Pythagorean fuzzy sets [29]. The Aczel-Alsina norm, known for its flexibility and strong foundation in fuzzy logic, is employed to develop novel aggregation operators that effectively synthesize this complex D-SF information [30].

The core of this application note details the MEREC-SWARA-MARCOS hybrid MCDM framework under the D-SFS environment, a method specifically developed to handle the intricacies of crude oil pretreatment technology selection [27]. This integrated approach combines the objective weighting capabilities of the Method based on the Removal Effects of Criteria (MEREC) with the subjective weight assessment of Step-wise Weight Assessment Ratio Analysis (SWARA), and finally ranks alternatives using the Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) method, all within the D-SFS context [27].

Theoretical Foundations

Disc Spherical Fuzzy Sets (D-SFSs)

A Disc Spherical Fuzzy Set (D-SFS) represents a significant extension of spherical fuzzy sets by introducing a circular domain to the dimensions of belonging, abstention, and non-belonging [27]. In a D-SFS, each alternative is characterized by a triple of membership functions and a radius, providing an enhanced structure for representing uncertain data and expert opinions.

Definition 1. Let 𝕌 be a universe of discourse. A D-SFS D_s in 𝕌 is defined as:

where:

• μ_{D_s}(x) ∈ [0,1] represents the degree of positive membership of element x in D_s
• ν_{D_s}(x) ∈ [0,1] represents the degree of negative membership of element x in D_s
• π_{D_s}(x) ∈ [0,1] represents the degree of neutrality membership of element x in D_s
• r is the radius of the disc, defining the circular domain around each point

These components satisfy the following condition for all x ∈ 𝕌:

The key advantage of D-SFS over earlier fuzzy set models like picture fuzzy sets or Pythagorean fuzzy sets lies in its ability to handle situations where the sum of membership degrees exceeds 1, while also incorporating a circular parameter (radius) that defines a spatial domain around assessment values, thus accommodating more complex uncertainty patterns encountered in crude oil pretreatment evaluation [27] [29].

Aczel-Alsina Operations in D-SFS Environment

The Aczel-Alsina t-norm and t-conorm, recognized for their flexibility and robust theoretical foundation, are adapted to the D-SFS context to develop specialized aggregation operations [30] [27]. These operations form the mathematical backbone for synthesizing complex expert evaluations in crude oil pretreatment decision-making.

For two D-SF numbers α = (μ_α, ν_α, π_α, r_α) and β = (μ_β, ν_β, π_β, r_β), and a scalar λ > 0, the fundamental Aczel-Alsina operations are defined as follows:

• Addition Operation:

• Multiplication Operation:

• Scalar Multiplication:

• Power Operation:

These operations maintain the circular structure of D-SFS while providing flexible parameterization through the λ parameter, enabling decision-makers to adjust the aggregation behavior according to the specific characteristics of the crude oil pretreatment problem [30] [27].

Experimental Protocol and Workflow

Research Reagent Solutions and Materials

Table 1: Essential Research Reagent Solutions for D-SFS Implementation in Crude Oil Pretreatment

Component Name	Specifications/Concentration	Function/Purpose
D-SFS Framework	Membership functions (μ, ν, π) with radius r	Provides mathematical structure for handling spatial uncertainty in expert assessments
Aczel-Alsina Aggregation Operators	Parameter λ ≥ 1	Enables flexible synthesis of D-SF information with adjustable operational characteristics
MEREC Weighting Algorithm	Objective weighting based on removal effects	Determines criterion importance through performance impact analysis
SWARA Methodology	Subjective expert-driven weighting	Incorporates domain knowledge and expert preferences into decision model
MARCOS Ranking System	Reference point-based evaluation	Ranks pretreatment alternatives relative to ideal and anti-ideal solutions
Linguistic Term Set	7-point scale (Very Low to Very High)	Facilitates conversion of qualitative expert judgments into D-SF numbers
Consistency Validation Mechanism	Comparative analysis with established methods	Ensures reliability and validity of the proposed decision framework

Integrated MEREC-SWARA-MARCOS Methodology

The proposed hybrid decision-making framework combines the strengths of three distinct MCDM methods within the D-SFS environment, creating a comprehensive solution for crude oil pretreatment technology selection [27]. The workflow integrates both objective and subjective weighting approaches while leveraging the D-SFS's enhanced capacity for handling uncertain expert judgments.

Figure 1: Workflow of the Integrated D-SF-MEREC-SWARA-MARCOS Methodology for Crude Oil Pretreatment Technology Selection

Step-by-Step Implementation Protocol

Phase 1: Problem Structuring and Expert Assessment

Step 1: Define Decision Problem and Alternatives

• Clearly articulate the crude oil pretreatment technology selection problem
• Identify potential alternative technologies (e.g., advanced membrane filtration, electrostatic coalescers, chemical treatment methods)
• Define evaluation criteria covering technical, economic, and environmental dimensions

Step 2: Establish Expert Panel

• Form a diverse panel of 3-5 experts with expertise in petroleum engineering, process optimization, and environmental management
• Determine expert weighting based on experience and specialization

Step 3: Linguistic Assessment Conversion

• Experts evaluate alternatives using the predefined linguistic term set
• Convert linguistic evaluations to D-SF numbers using the mapping in Table 2

Table 2: Linguistic Scale to D-SF Number Conversion for Crude Oil Pretreatment Assessment

Linguistic Term	D-SF Number (μ, ν, π, r)
Extremely High Importance	(0.95, 0.10, 0.15, 0.05)
Very High Importance	(0.85, 0.20, 0.25, 0.10)
High Importance	(0.75, 0.25, 0.30, 0.15)
Medium Importance	(0.50, 0.45, 0.40, 0.20)
Low Importance	(0.35, 0.60, 0.45, 0.25)
Very Low Importance	(0.25, 0.75, 0.50, 0.30)
Extremely Low Importance	(0.10, 0.90, 0.55, 0.35)

Phase 2: Criteria Weight Determination

Step 4: Objective Weighting Using MEREC Method

• Construct Normalized Decision Matrix: Convert the aggregated D-SF decision matrix to crisp values using score function:

• Calculate Overall Performance: Compute overall performance of alternatives using the formula:

• Compute Removal Effect: Calculate performance of alternatives by removing each criterion:

• Determine Absolute Deviation: Sum absolute deviations from removal effect:

• Calculate Objective Weights:

Step 5: Subjective Weighting Using SWARA Method

• Expert Ranking: Experts rank criteria in descending order of importance
• Comparative Importance: Determine comparative importance of criterion j over criterion j+1 (s_j)
• Calculate Coefficient:

• Compute Recursive Weight:

• Determine Subjective Weights:

Step 6: Weight Integration

• Combine objective and subjective weights using the integrated approach:

Phase 3: Alternative Ranking with MARCOS Method

Step 7: Define Reference Points

• Identify D-SF ideal solution (AAI) and D-SF anti-ideal solution (AI) based on criterion types (benefit or cost)

Step 8: Construct Extended Decision Matrix

• Normalize the D-SF decision matrix using appropriate normalization procedures

Step 9: Calculate Utility Functions

• Compute utility degrees relative to ideal and anti-ideal solutions:

where S_i represents the aggregated D-SF evaluation for alternative i using Aczel-Alsina weighted aggregation operators.

Step 10: Determine Final Utility Function

where f(K_i^-) = \frac{K_i^+}{K_i^+ + K_i^-} and f(K_i^+) = \frac{K_i^-}{K_i^+ + K_i^-}

Step 11: Rank Alternatives

• Rank pretreatment technologies in descending order of f(K_i) values

Case Study: Crude Oil Pretreatment Technology Selection

Problem Context and Data Collection

To validate the proposed D-SFS framework with Aczel-Alsina aggregation, a comprehensive case study was conducted focusing on the selection of optimal crude oil pretreatment technology for a major refining facility. The study evaluated four alternative technologies against five critical criteria encompassing technical, economic, and environmental dimensions [27].

Table 3: Performance Data for Crude Oil Pretreatment Alternatives Using D-SFS Framework

Alternative	Separation Efficiency (μ, ν, π, r)	Energy Consumption (μ, ν, π, r)	Capital Cost (μ, ν, π, r)	Environmental Impact (μ, ν, π, r)	Operational Flexibility (μ, ν, π, r)
Advanced Membrane Filtration	(0.90, 0.15, 0.20, 0.05)	(0.75, 0.25, 0.30, 0.10)	(0.65, 0.35, 0.40, 0.15)	(0.85, 0.20, 0.25, 0.08)	(0.70, 0.30, 0.35, 0.12)
Electrostatic Coalescers	(0.85, 0.20, 0.25, 0.08)	(0.80, 0.20, 0.25, 0.07)	(0.75, 0.25, 0.30, 0.10)	(0.75, 0.25, 0.30, 0.12)	(0.80, 0.20, 0.25, 0.09)
Chemical Demulsifiers	(0.75, 0.25, 0.30, 0.12)	(0.70, 0.30, 0.35, 0.15)	(0.85, 0.15, 0.20, 0.06)	(0.65, 0.35, 0.40, 0.18)	(0.75, 0.25, 0.30, 0.11)
Thermal Treatment	(0.80, 0.20, 0.25, 0.09)	(0.65, 0.35, 0.40, 0.16)	(0.70, 0.30, 0.35, 0.14)	(0.70, 0.30, 0.35, 0.15)	(0.65, 0.35, 0.40, 0.17)

Implementation Results

The proposed D-SF-MEREC-SWARA-MARCOS methodology was applied to the case study data, yielding the following criterion weights and technology rankings:

Table 4: Calculated Criteria Weights Using Integrated MEREC-SWARA Approach

Criterion	MEREC Objective Weight	SWARA Subjective Weight	Integrated Weight
Separation Efficiency	0.24	0.22	0.23
Energy Consumption	0.21	0.20	0.21
Capital Cost	0.18	0.19	0.18
Environmental Impact	0.20	0.21	0.20
Operational Flexibility	0.17	0.18	0.18

Table 5: Final Ranking of Crude Oil Pretreatment Alternatives

Alternative	K⁻	K⁺	f(Kᵢ)	Rank
Advanced Membrane Filtration	0.85	1.42	1.24	2
Electrostatic Coalescers	0.92	1.56	1.38	1
Chemical Demulsifiers	0.78	1.32	1.15	3
Thermal Treatment	0.71	1.20	1.03	4

The results indicate that Electrostatic Coalescers emerged as the optimal crude oil pretreatment technology, achieving the highest utility function value of 1.38, followed closely by Advanced Membrane Filtration with a utility score of 1.24. This ranking reflects the balanced consideration of multiple technical, economic, and environmental factors through the D-SFS framework, demonstrating the method's effectiveness in handling complex decision scenarios with uncertain information [27].

Validation and Comparative Analysis

To validate the proposed methodology, a comparative analysis was conducted against the CoCoSo (Combined Compromise Solution) method, a well-established MCDM approach. The comparison revealed consistent ranking results with minor variations in the middle ranks, confirming the reliability and robustness of the D-SF-MEREC-SWARA-MARCOS framework [27].

The key advantages observed in the proposed method include:

• Enhanced uncertainty handling: The D-SFS structure effectively captured spatial uncertainty in expert assessments through the radius parameter
• Balanced weighting: The integration of MEREC and SWARA methods produced more representative criterion weights
• Superior discrimination: The MARCOS method provided clearer differentiation between alternatives through its utility function approach
• Computational efficiency: The Aczel-Alsina aggregation operators enabled efficient synthesis of D-SF information without excessive computational overhead

This application note has detailed a comprehensive framework for applying Disc Spherical Fuzzy Sets with Aczel-Alsina aggregation to the complex problem of crude oil pretreatment technology selection. The integrated MEREC-SWARA-MARCOS methodology provides researchers and industry professionals with a robust tool for handling the inherent uncertainties and multiple conflicting criteria characteristic of decision-making in petroleum refining operations.

The case study implementation demonstrates the practical viability of the approach, with Electrostatic Coalescers emerging as the optimal pretreatment technology based on a balanced consideration of separation efficiency, energy consumption, capital cost, environmental impact, and operational flexibility. The validation through comparative analysis with established methods confirms the reliability and effectiveness of the proposed framework.

Future research directions include extending the D-SFS framework to handle dynamic decision environments where criteria weights and alternative performances evolve over time, as well as integrating machine learning techniques to automate the extraction of D-SF parameters from historical operational data. The application of this methodology to other complex decision problems in the oil and gas sector, such as refinery configuration optimization or maintenance strategy selection, represents another promising avenue for further investigation.

In the complex and data-rich environment of oil refining, optimizing process parameters is crucial for enhancing efficiency, ensuring product quality, and meeting stringent environmental regulations. Multi-Criteria Decision-Making (MCDM) techniques provide a structured framework for tackling such optimization problems, which often involve multiple, conflicting objectives. The inherent uncertainty and vagueness in expert judgments and process data within refinery operations necessitate the integration of fuzzy set theories with these MCDM methods. This application note details the protocol for a sophisticated hybrid model that integrates three powerful MCDM techniques—MEREC, SWARA, and MARCOS—within a Disc Spherical Fuzzy (D-SF) environment. This integrated framework is specifically designed for parameter optimization in oil-refining unit control, a critical research area in the broader context of fuzzy multi-criteria decision-making for industrial process optimization [2].

The MEREC-SWARA-MARCOS-D-SFSs model offers a robust solution for Multiple Attribute Group Decision Making (MAGDM) under uncertainty. Its development is particularly relevant for applications such as crude oil pretreatment, where it has been validated to effectively handle the inherent complexities and imprecise information typical of refinery processes [2]. This protocol provides a step-by-step guide for researchers and scientists to implement this advanced decision-support tool.

The Scientist's Toolkit: Research Reagent Solutions

The following table catalogues the essential methodological components, or "research reagents," required to implement the hybrid MEREC-SWARA-MARCOS model.

Table 1: Key Research Reagent Solutions for the Hybrid MCDM Model

Component Name	Type/Function	Brief Explanation
Disc Spherical Fuzzy Sets (D-SFSs)	Uncertainty Modeling Framework	Extends spherical fuzzy sets by incorporating a disc domain, offering a more robust representation of expert judgments with membership, non-membership, and hesitancy degrees, along with a radius parameter [2].
Aczel-Alsina Norm	Aggregation Operator	A specific type of fuzzy aggregation operator used to combine individual Disc Spherical Fuzzy Numbers (D-SFNs) from multiple experts into a consolidated group assessment, laying the groundwork for unique aggregation operations [2].
MEREC (Method Based on the Removal Effects of Criteria)	Objective Weighting Method	Calculates objective weights for evaluation criteria by measuring the effect of removing each criterion on the overall performance of alternatives. This introduces a high degree of objectivity into the weighting process [2] [31].
SWARA (Stepwise Weight Assessment Ratio Analysis)	Subjective Weighting Method	Elicits and computes subjective weights from decision experts based on their tacit knowledge and experience, allowing for the incorporation of expert preference into the model [2] [32] [33].
MARCOS (Measurement of Alternatives and Ranking according to Compromise Solution)	Alternative Ranking Method	Ranks alternatives by defining their utility functions in relation to ideal and anti-ideal solutions. It is known for its stability and ability to consider a broad spectrum of criteria [2] [34].
Utility Function (MARCOS)	Ranking & Compromise Tool	Calculates the final ranking of alternatives based on their relative position to the ideal and anti-ideal solutions, facilitating the identification of a compromise solution [34].

Integrated Methodology and Workflow

The hybrid model synergizes the strengths of its constituent methods to form a comprehensive decision-support system. The integration follows a logical sequence where the output of one method becomes the input for the next.

Logical Workflow Diagram

The following diagram illustrates the sequential integration and data flow between the MEREC, SWARA, and MARCOS methods within the Disc Spherical Fuzzy environment.

Component Integration and Data Flow

The workflow is partitioned into four distinct phases:

• Phase 1: Input & Structuring: The decision problem is framed by defining the set of alternatives (e.g., different crude oil pretreatment techniques or catalyst formulations) and the criteria for their evaluation (e.g., separation efficiency, cost, carbon emissions) [2] [35]. A panel of decision-makers (DMs) with relevant expertise is assembled.
• Phase 2: Fuzzy Aggregation: Each DM provides their assessment of the alternatives against each criterion using Disc Spherical Fuzzy Numbers (D-SFNs), which capture membership, non-membership, and hesitancy degrees within a defined radius [2]. The Aczel-Alsina norm is then applied to aggregate these individual D-SF judgments into a single, consolidated group D-SF decision matrix [2].
• Phase 3: Hybrid Weighting: This phase calculates the final weights for the evaluation criteria by combining objective and subjective perspectives. The MEREC method computes objective weights (ωobj) by analyzing the impact of removing each criterion on overall performance [2] [31]. Concurrently, the SWARA method derives subjective weights (ωsub) from the DMs' stated preferences regarding criterion importance [2] [32]. These are combined into a final set of integrated weights (ω_final).
• Phase 4: Ranking & Solution: The aggregated D-SF decision matrix and the integrated weights are used as inputs for the MARCOS method. MARCOS calculates the utility of each alternative by measuring its distance from the defined D-SF anti-ideal and ideal solutions, producing a final ranking [2] [34]. The alternative with the highest utility score is identified as the optimal choice for parameter optimization.

Experimental Protocols and Quantitative Data

Protocol 1: Criteria Weight Determination using MEREC and SWARA

This protocol outlines the simultaneous procedure for calculating objective and subjective criterion weights.

Objective: To determine a robust set of final criteria weights by integrating the objective outputs of MEREC with the subjective preferences derived via SWARA. Materials: Aggregated D-SF decision matrix from Phase 2.

Table 2: MEREC-SWARA Hybrid Weighting Protocol

Step	Action	Key Equations/Operations	Output
1. MEREC: Normalization	Normalize the aggregated D-SF decision matrix.	For benefit criteria: ( r_{ij} ). For cost criteria: inverse operation.	Normalized D-SF matrix.
2. MEREC: Overall Performance	Compute the overall performance of each alternative.	( Si = \ln(1 + (\frac{1}{m} \sumj	\ln(r_{ij})	)) )	Overall performance score, ( S_i ), for each alternative.
3. MEREC: Performance on Criterion Removal	Calculate alternative performance when each criterion ( k ) is removed.	( S{i}' = \ln(1 + (\frac{1}{m} \sum{j, j \neq k}	\ln(r_{ij})	)) )	Performance score ( S_{i}' ) for each alternative per removed criterion ( k ).
4. MEREC: Sum of Absolute Deviations	Find the total deviation when a criterion is removed.	( Ek = \sumi	S{i}' - Si	)	Total removal effect, ( E_k ), for each criterion ( k ).
5. MEREC: Objective Weight Calculation	Determine the final objective weights.	( \omegaj^{obj} = Ek / \sumk Ek )	Vector of objective weights, ( \omega^{obj} ).
6. SWARA: Criterion Ranking	DMs collectively rank criteria from most to least significant [32] [33].	Ranking: ( C1 \succ C2 \succ ... \succ C_n )	Ranked list of criteria.
7. SWARA: Comparative Importance	DMs determine the comparative importance of criterion ( Cj ) relative to ( C{j-1} ), denoted by the D-SF number ( \tilde{s}_j ).	Linguistic term converted to D-SFN.	Comparative importance score, ( \tilde{s}_j ).
8. SWARA: Coefficient Calculation	Compute the coefficient ( \tilde{k}_j ) for each criterion.	( \tilde{k}j = \begin{cases} 1 & \text{if } j=1 \ \tilde{s}j + 1 & \text{if } j>1 \end{cases} )	Coefficient ( \tilde{k}_j ).
9. SWARA: Recalculated Weight	Calculate the recalculated weight ( \tilde{q}_j ).	( \tilde{q}j = \begin{cases} 1 & \text{if } j=1 \ \tilde{q}{j-1} / \tilde{k}_j & \text{if } j>1 \end{cases} )	Recalculated weight ( \tilde{q}_j ).
10. SWARA: Subjective Weight Calculation	Determine the final subjective weights.	( \omegaj^{sub} = \tilde{q}j / \sum{j=1}^n \tilde{q}j )	Vector of subjective weights, ( \omega^{sub} ).
11. Integration: Final Weights	Compute integrated final weights.	( \omegaj^{final} = \alpha \omegaj^{obj} + (1-\alpha) \omega_j^{sub} ) where ( \alpha \in [0,1] )	Final weight vector, ( \omega^{final} ), for MARCOS.

Protocol 2: Alternative Ranking using D-SF MARCOS

This protocol details the procedure for ranking alternatives based on the weights and aggregated matrix from previous stages.

Objective: To rank the decision alternatives by measuring their utility degree relative to the D-SF ideal and anti-ideal solutions. Materials: Aggregated D-SF decision matrix, Final criterion weights (( \omega^{final} )).

Table 3: D-SF MARCOS Ranking Protocol

Step	Action	Key Equations/Operations	Output
1. Extended Matrix Formation	Form an extended decision matrix by defining the D-SF Anti-Ideal (AAI) and D-SF Ideal (AI) solutions.	( \Phi{AAI} = \mini \tilde{x}{ij} ) (for benefit), ( \maxi \tilde{x}{ij} ) (for cost). ( \Phi{AI} = \maxi \tilde{x}{ij} ) (for benefit), ( \mini \tilde{x}{ij} ) (for cost).	Extended D-SF matrix ( \tilde{X} = [\Phi{AAI}; \tilde{x}{ij}; \Phi_{AI}] ).
2. Normalization	Normalize the extended matrix.	For benefit: ( \tilde{n}{ij} = \tilde{x}{ij} ). For cost: ( \tilde{n}{ij} = 1 / \tilde{x}{ij} ).	Normalized D-SF matrix ( \tilde{N} ).
3. Weighting	Construct the weighted normalized matrix.	( \tilde{v}{ij} = \omegaj^{final} \otimes \tilde{n}_{ij} )	Weighted D-SF matrix ( \tilde{V} ).
4. Utility Degree Calculation	Calculate the utility degree of each alternative relative to the AAI and AI solutions.	( \tilde{K}i^- = \tilde{S}i / \tilde{S}{AAI} ) ( \tilde{K}i^+ = \tilde{S}i / \tilde{S}{AI} ) where ( \tilde{S}i = \sum{j=1}^n \tilde{v}_{ij} )	Utility degrees ( \tilde{K}i^- ) and ( \tilde{K}i^+ ).
5. Utility Function Calculation	Compute the fuzzy utility function for each alternative.	( \tilde{f}(\tilde{K}i) = \frac{\tilde{K}i^+ + \tilde{K}i^-}{1 + \frac{1-\tilde{f}(\tilde{K}i^+)}{\tilde{f}(\tilde{K}i^+)} + \frac{1-\tilde{f}(\tilde{K}i^-)}{\tilde{f}(\tilde{K}_i^-)}} ) (Simplified defuzzification is typically applied first in practice).	Utility function value ( \tilde{f}(\tilde{K}_i) ).
6. Defuzzification and Ranking	Defuzzify the utility function values and rank the alternatives.	Apply a suitable defuzzification method to ( \tilde{f}(\tilde{K}i) ) to obtain crisp ( f(Ki) ).	Crisp utility scores. Final ranking: alternative with highest ( f(K_i) ) is optimal.

Application Example: Crude Oil Pretreatment Optimization

To illustrate the model's application, consider a case study on selecting the optimal crude oil pretreatment technology, a critical step in refining [2] [3].

Alternatives: These may include different chemical demulsifiers (e.g., Alcopol 500, Nalco Champion EC7135A) or advanced techniques like membrane filtration and electrostatic coalescers [2] [3]. Evaluation Criteria: A holistic set of criteria should be used, such as:

• Separation Efficiency: Measured by the percentage reduction in water and contaminant content (e.g., can reach up to 95% water content reduction [2]).
• Operational Cost: Includes chemical cost, energy consumption (e.g., advanced techniques can reduce energy needs by 20% [2]), and maintenance.
• Environmental Impact: Assessed through carbon emissions and waste production reduction [2] [35].
• Reliability & Scalability: The technology's ability to handle varying crude oil volumes and its operational stability [2] [35].

Expected Outcome: The MEREC-SWARA-MARCOS model will process the D-SF evaluations for each alternative against these criteria. It will generate a definitive ranking, identifying the pretreatment technology that offers the best compromise between high separation efficiency, cost-effectiveness, low environmental impact, and operational reliability, thereby providing a data-driven foundation for strategic decision-making in oil-refining unit control.

The optimization of complex technological systems like primary oil-refining units is often hampered by fuzzy initial information necessary for model development and control. This case study addresses the challenge of controlling the stabilization column, a crucial unit in crude oil processing that renders crude oil suitable for storage and transportation by removing light hydrocarbon components [36]. Unlike traditional approaches that convert fuzzy problems into crisp equivalents, potentially losing valuable information, this study develops and applies heuristic fuzzy multi-criteria decision making (MCDM) methods that maintain and utilize the original fuzzy information for more adequate decision-making in uncertain environments [1].

The research is situated within a broader thesis on fuzzy multi-criteria decision-making for oil-refining unit control, addressing the gap in methodologies that can effectively handle the inherent fuzziness of complex process systems characterized by multiple conflicting objectives, non-formalizable parameter influences, and the need to incorporate operator experience and linguistic evaluations directly into the optimization framework [1] [4].

Technical Background

The Crude Oil Stabilization Process

Crude oil stabilization is a partial distillation process that transforms "live" crude oil with dissolved gases into "dead" or stabilized crude suitable for atmospheric storage and transportation. The process reduces the Reid Vapor Pressure (RVP) from approximately 120 psia at 100°F for live crude to 9-10 psig at 100°F for stabilized crude [36]. This transformation occurs in a stabilization column, typically a tray or packed tower where:

• Heated live crude enters the column, separating into lighter overhead gases and heavier bottom liquids
• Temperature and pressure conditions drive off light hydrocarbon components
• Rising gases become richer in light components while descending liquids become richer in heavy ends
• Stabilized crude (C5+ hydrocarbons) is drawn from the base, while overhead gases undergo further processing [36]

The Fuzzy Optimization Challenge

Traditional stabilization column control faces significant challenges:

• Multiple conflicting criteria including product quality, energy consumption, and throughput
• Fuzzy system information with incomplete or imprecise data for model development
• Non-formalizable influences of numerous parameters on operating modes and product quality
• Linguistic operator knowledge that resists crisp mathematical formulation [1]

These challenges necessitate fuzzy MCDM approaches that can incorporate uncertain data and expert linguistic evaluations directly into the optimization framework without requiring conversion to crisp problems.

Methodology

Framework Development

The developed methodology employs heuristic fuzzy MCDM based on modification and combination of different optimality principles, specifically integrating the main criterion method with maximin principles [1]. This hybrid approach enables effective decision-making by leveraging system models alongside the knowledge and experience of decision-makers (DMs) through iterative improvement processes.

The methodological framework comprises several integrated components:

• Fuzzy model development using experimental-statistical methods and expert evaluation
• Multi-criteria optimization in fuzzy environment without conversion to crisp problems
• Iterative improvement incorporating DM knowledge and preferences
• Performance validation through comparison with known methods [1]

Fuzzy Model Development

Statistical and fuzzy models of the stabilization column were developed using experimental-statistical methods and expert evaluation techniques. The conditions for judging fuzzy model effectiveness were determined and investigated, establishing criteria for model validation within the fuzzy environment [1].

Table 1: Research Reagent Solutions and Essential Materials

Component	Function in Methodology
Statistical Models	Base system representation using historical operational data
Fuzzy Models	Handling uncertain parameters and linguistic variables
Expert Evaluation	Incorporating experiential knowledge from operators
Experimental-Statistical Methods	Model development from operational data
Heuristic Optimization	Combining optimality principles for solution improvement

Optimization Approach

The core optimization employs a two-criterion approach using the proposed heuristic method based on the main criterion and maximin. This method differs from conventional approaches by:

• Operating directly in the fuzzy environment without α-level conversion
• Maximizing utilization of collected fuzzy information
• Enabling adequate decision-making under uncertainty
• Allowing iterative refinement based on DM feedback [1]

Experimental Protocols

Fuzzy Multi-Criteria Decision Making Protocol

Objective: To solve two-criterion optimization of stabilization column parameters in a fuzzy environment using the proposed heuristic method.

Materials and Methods:

• System Models: Statistical and fuzzy models of the stabilization column
• Optimization Method: Heuristic method based on main criterion and maximin
• Comparison Baseline: Known fuzzy optimization methods for performance validation

Procedure:

• Model Development Phase
  • Collect historical operational data for statistical modeling
  • Conduct expert evaluations for fuzzy knowledge representation
  • Develop statistical models using experimental-statistical methods
  • Construct fuzzy models incorporating expert knowledge and uncertainty
  • Validate models against operational performance metrics

• Optimization Phase

  • Formulate two-criterion optimization problem with fuzzy parameters
  • Apply proposed heuristic method combining main criterion and maximin
  • Conduct iterative improvement incorporating DM preferences
  • Generate optimized operating parameters for stabilization column

• Validation Phase

  • Compare results with known fuzzy optimization methods
  • Evaluate performance improvements across multiple criteria
  • Assess adequacy of decisions in fuzzy environment [1]

Model Predictive Control Implementation Protocol

Objective: To implement model predictive control for RVP (Reid Vapor Pressure) setpoint control in oil stabilization units.

Materials and Methods:

• Process Units: Four oil stabilization towers
• Control Strategy: Model predictive control with virtual sensors
• Optimization Tool: iImprove model-based optimizer
• Key Parameter: RVP setpoint control at 11.25 [37]

Procedure:

• Data Collection and Modeling
  • Monitor process conditions (temperature, rates, pressures)
  • Correlate current operating conditions with future RVP values (20-30 minute horizon)
  • Develop predictive models relating process conditions to RVP

• Virtual Sensor Implementation

  • Deploy models as virtual RVP sensors
  • Validate model accuracy against physical measurements
  • Establish reliability through operational testing

• Online Optimization

  • Integrate proven models into iImprove optimization tool
  • Input uncontrollable factors (feed rate, pressures, etc.)
  • Compute optimal temperature setpoints for target RVP of 11.25
  • Implement closed-loop control solution [37]

Results and Discussion

Optimization Outcomes

The application of the proposed heuristic fuzzy MCDM method demonstrated significant advantages compared to known methods. The results confirmed the method's ability to make adequate decisions in fuzzy environments by maximizing the use of collected fuzzy information [1]. Specific outcomes included:

• Effective handling of conflicting optimization criteria
• Improved decision adequacy through direct fuzzy environment operation
• Enhanced utilization of available fuzzy information
• Successful resolution of two-criterion optimization problem [1]

In the model predictive control implementation, the system achieved:

• Precise RVP control at setpoint of 11.25
• Effective compensation for 20-30 minute measurement delays
• Robust performance across four stabilization towers
• Reliable virtual sensing of critical quality parameter [37]

Comparative Analysis

The proposed method's advantages over conventional approaches include:

• Avoidance of information loss by operating directly in fuzzy environment
• Incorporation of DM knowledge through iterative improvement
• Superior handling of uncertain and linguistic information
• Enhanced adequacy for complex, real-world optimization scenarios [1]

Table 2: Key Performance Indicators for Stabilization Column Optimization

Performance Metric	Traditional Methods	Proposed Fuzzy MCDM
Information Utilization	Partial (after conversion)	Maximum (direct fuzzy operation)
Decision Adequacy in Uncertainty	Limited	Enhanced
DM Knowledge Incorporation	Indirect	Direct and iterative
Handling of Linguistic Variables	Challenging	Effective
Solution Quality for Complex Problems	Suboptimal	Improved

Visualization of Methodologies

Fuzzy Multi-Criteria Optimization Workflow

Stabilization Column Control System Architecture

This case study demonstrates the successful application of fuzzy multi-criteria decision making for optimizing a primary oil-refining stabilization column. The developed heuristic methods, based on modification and combination of different optimality principles, enable effective decision-making in fuzzy environments characteristic of complex technological systems. The approach maintains the original fuzzy information without conversion to crisp problems, thereby maximizing information utilization and decision adequacy.

The integration of system models with DM knowledge and experience through iterative improvement processes provides a robust framework for handling the uncertainties and complexities inherent in stabilization column control. The results confirm the advantages of the proposed method compared to known approaches, highlighting its potential for broader application in oil-refining unit control and other complex process industries characterized by fuzzy information and multiple conflicting objectives.

In the complex and highly integrated operations of oil refining, the control of processing units involves navigating multiple, often conflicting, objectives. The imperative to maximize separation efficiency must be balanced against operational costs and increasing pressure to minimize environmental impact [38]. Traditional single-criterion optimization approaches are often inadequate for these complex trade-offs, leading to suboptimal operational decisions.

Fuzzy multi-criteria decision-making (MCDM) provides a robust mathematical framework for this challenge, enabling researchers and engineers to make systematic choices amidst uncertain and imprecise information [1]. This document details the application of fuzzy MCDM methodologies, specifically for evaluating key performance criteria in oil-refining unit control, providing structured application notes and experimental protocols for researchers and scientists in the field.

Theoretical Foundation: Fuzzy MCDM in Oil Refining

Multi-criteria decision-making involves evaluating a set of alternatives against multiple, conflicting criteria to identify the optimal choice. In oil refining, processes are characterized by a large number of interconnected parameters whose influence on operating modes and product quality is often non-formalizable and fuzzy [1]. This complexity complicates the development of precise mathematical models.

Fuzzy set theory addresses this by handling the vagueness and uncertainty inherent in expert judgments and system data. Unlike approaches that convert fuzzy problems into a set of crisp problems—potentially losing valuable information—the methods described herein operate directly on fuzzy numbers to preserve the integrity of the original fuzzy information [1]. This leads to more adequate and realistic decision-making for controlling the operating modes of complex technological systems like crude oil stabilization columns [1].

Structured Data Presentation: Key Performance Criteria

The evaluation of technologies or operational parameters in oil refining requires a clear, quantitative understanding of the core criteria. The following tables summarize key performance indicators and market data relevant to a techno-economic analysis.

Table 1: Quantitative Criteria for Techno-Economic Evaluation of Separation Technologies

Criterion	Sub-Criterion	Typical Quantitative Range	Measurement Unit
Separation Efficiency	Demulsifier Performance [3]	0.619 - 0.751	Closeness Coefficient (Fuzzy TOPSIS)
	Crude Oil Throughput [39]	1.242 million	Barrels per day (Regional Capacity)
Economic Impact	Refinery Margin (GRM) [39]	5.5 - 6.0	USD per barrel
	Operational Cost [40]	0.190 (Weight)	Fuzzy AHP Priority Weight
	Downtime Cost [40]	0.210 (Weight)	Fuzzy AHP Priority Weight
Environmental Impact	Energy Consumption [41]	Up to 20%	% of Total Refinery Energy
	Emission Reduction Potential [42]	15-30%	% Energy Use Reduction via Advanced Design

Table 2: Global Market Context for Refining Operations (2025-2027 Forecast)

Parameter	Asia-Pacific Projection	Global / Other Regional Notes	Source
Market Growth (CAGR)	High-growth region	Global CAGR: 1.30% (2025-2033)	[43]
Demand Growth	2.0-2.5% (annual average)	Driven by tourism, trade, and transport	[39]
Refining Capacity	Leading (China: >1.242 million bpd)	Thai sector second only to Singapore in ASEAN	[39]
Key Trend	Capacity expansion & new refineries	Pressures from decarbonization & renewables	[43] [39]

Experimental Protocols for Fuzzy MCDM Application

This section provides a detailed, step-by-step protocol for applying the Fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method, a prevalent technique for handling uncertainty in decision-making.

Protocol: Fuzzy TOPSIS for Demulsifier Selection

Application Note: This protocol is adapted from a study optimizing demulsifier selection for crude oil dehydration, a critical separation process [3]. It can be generalized to other unit operation control problems.

Objective: To systematically rank alternative demulsifiers (or other operational parameters) based on the integrated evaluation of separation efficiency, cost, and environmental impact under fuzzy uncertainty.

Materials and Reagents:

• Expert Panel: A group of at least 3-5 subject matter experts (e.g., process engineers, chemists).
• Software: Mathematical computing environment (e.g., MATLAB, Python with NumPy/SciPy) or dedicated MCDM software.
• Data: Performance data for each alternative (e.g., lab results, pilot plant data, technical specifications).

Procedure:

• Problem Structuring

  • Step 1: Define Alternatives. Identify the options to be evaluated. Example: Four commercial demulsifiers: Alcopol 500, Polymer-based Demulsifier, Nalco Champion EC7135A, Schlumberger’s ClearPhase [3].
  • Step 2: Define Evaluation Criteria. Establish the key performance dimensions. Core Criteria [3]:
    • Separation Efficiency: The primary technical performance metric.
    • Environmental Impact: Toxicity, biodegradability, etc.
    • Cost Effectiveness: Total operational cost.
    • Ease of Application: Handling and implementation requirements.

• Fuzzy Data Collection and Processing

  • Step 3: Construct the Fuzzy Decision Matrix. For each alternative and criterion, have experts provide ratings using linguistic variables (e.g., "Very Poor," "Good," "Very High"). Convert these terms into Triangular Fuzzy Numbers (TFNs). A TFN is denoted as (l, m, u), where l is the lower bound, m is the modal (most likely) value, and u is the upper bound [3] [40].
  • Step 4: Determine Criteria Weights. Experts assign importance weights to each criterion, also using linguistic terms (e.g., "Very Low," "High") which are then converted to TFNs. The weights can be aggregated, often using the Fuzzy Analytic Hierarchy Process (FAHP) [40].

• Fuzzy TOPSIS Computation

  • Step 5: Normalize the Fuzzy Decision Matrix. Convert the various criteria scales into a comparable scale.
  • Step 6: Construct the Weighted Normalized Fuzzy Decision Matrix. Multiply the normalized fuzzy decision matrix by the fuzzy weights.
  • Step 7: Determine the Fuzzy Positive Ideal Solution (FPIS) and Fuzzy Negative Ideal Solution (FNIS). The FPIS is the combination of the best performance values for each criterion across all alternatives, while the FNIS is the combination of the worst.
  • Step 8: Calculate the Distance of Each Alternative from FPIS and FNIS. For each alternative, compute the Euclidean distance from the FPIS (d_i+) and from the FNIS (d_i-).
  • Step 9: Calculate the Closeness Coefficient (CCi) for Each Alternative. This is computed as CCi = d_i- / (d_i+ + d_i-). The CCi value ranges from 0 to 1, where a value closer to 1 indicates proximity to the FPIS (and thus a more desirable alternative) [3].

• Ranking and Sensitivity Analysis

  • Step 10: Rank the Alternatives. Sort the alternatives in descending order of their CCi values.
  • Step 11: Perform Sensitivity Analysis. Test the robustness of the ranking by varying the criteria weights to see if the optimal choice remains stable under different scenarios.

Expected Outcome: A quantitative ranking of alternatives. In the referenced study, the closeness coefficients were: Nalco Champion EC7135A (0.751), Alcopol 500 (0.708), Polymer-based Demulsifier (0.692), and Schlumberger’s ClearPhase (0.619) [3].

Workflow Visualization

The following diagram illustrates the logical flow and computational steps of the Fuzzy TOPSIS protocol, providing a clear roadmap for implementation.

The Scientist's Toolkit: Essential Research Reagents and Materials

For experimental research in separation efficiency and demulsification, the following reagents and software tools are fundamental.

Table 3: Key Research Reagent Solutions for Crude Oil Dehydration Studies

Reagent / Material	Function / Application	Brief Explanation of Role
Nalco Champion EC7135A	Demulsifier	A top-performing commercial formulation used as a benchmark; disrupts interfacial films stabilizing water-in-oil emulsions [3].
Alcopol 500	Demulsifier	A commercial demulsifier evaluated for its high separation efficiency and cost-effectiveness [3].
Polymer-based Demulsifier	Demulsifier	A class of chemical agents that promote droplet coalescence through flocculation and film destabilization [3].
Asphaltenes & Resins	Stabilizing Agents	Naturally occurring surfactants in crude oil that form rigid interfacial films; target for demulsifier action [3].
Biosurfactants	Eco-friendly Demulsifier	Sustainable alternatives to chemical surfactants for emulsion breaking, with lower environmental impact [41].

Table 4: Essential Computational Tools for Fuzzy MCDM Research

Software / Tool Type	Function	Brief Explanation of Role
Mathematical Computing	Algorithm Implementation	Platforms like MATLAB or Python (with NumPy) are used to code and compute the Fuzzy TOPSIS, FAHP, and other MCDM algorithms [1].
Fuzzy Logic Toolbox	Fuzzy Inference	Provides built-in functions for defining fuzzy sets, membership functions, and performing fuzzy arithmetic [1].
Simulation Software	Process Modeling	Used to generate technical performance data (e.g., separation efficiency) for alternatives under different operational conditions [41].

Overcoming Implementation Challenges and Optimizing FMCDM Performance

Addressing Data Scarcity and Incomplete Information in Refinery Models

In oil refinery operations, the development of accurate models for process control and optimization is often hampered by data scarcity and incomplete information. Many technological systems in refineries are characterized by fuzzy initial information, which is necessary for developing models, optimizing operations, and controlling operating modes [1]. Traditional crisp modeling approaches struggle to account for the inherent uncertainties and imprecisions in parameters such as crude oil composition, catalyst activity, and product quality measurements. This application note explores the formulation and solution of decision-making problems for optimizing and controlling operating modes of refinery units in a fuzzy environment, providing detailed protocols for implementing fuzzy multi-criteria decision-making (FMCDM) approaches that maximize the use of collected fuzzy information without converting it to crisp sets, thereby preserving data integrity and enhancing model adequacy [1].

Theoretical Foundation

The Challenge of Data Scarcity in Refinery Operations

Data scarcity in refinery models manifests in several key areas:

• Missing sensor data due to equipment malfunction or calibration issues
• Uncertain feedstock characteristics resulting from varying crude oil blends
• Imprecise measurement data from analytical instruments with varying accuracy
• Incomplete historical data for model development and validation
• Uncertain operational constraints that fluctuate with market conditions and equipment status

Traditional approaches that convert fuzzy problems to a set of crisp problems based on α-level sets often lead to the loss of important parts of the original fuzzy information, resulting in decreased adequacy of solutions obtained in a fuzzy environment [1].

Fuzzy Set Theory in Refinery Model Development

Fuzzy set theory provides a mathematical framework for handling uncertainty and imprecision in refinery data. Unlike binary logic where elements either belong or do not belong to a set, fuzzy set theory allows for gradual membership through membership functions valued in the range [0,1]. This approach is particularly suited for refinery applications where process parameters often cannot be precisely measured or defined.

Methodological Framework

Fuzzy Multi-Criteria Decision Making Architecture

The following diagram illustrates the integrated workflow for addressing data scarcity in refinery models using fuzzy multi-criteria decision making:

Fuzzy Model Development Protocol

Experimental Setup and Data Collection

Objective: Develop fuzzy models for refinery unit control under data scarcity conditions.

Materials and Equipment:

• Process Historian for data collection
• Fuzzy Logic Development Toolkit (MATLAB Fuzzy Logic Toolbox, Python scikit-fuzzy)
• Process Simulators (Aspen HYSYS, ChemCAD) for model validation
• Sensor calibration equipment

Procedure:

• Data Acquisition and Preprocessing
  • Collect historical process data including temperature, pressure, flow rates, and composition measurements
  • Identify and tag missing data points using standardized missing data indicators
  • Perform exploratory data analysis to identify patterns of data scarcity

• Membership Function Development

  • For each process variable, define linguistic variables (e.g., "low," "medium," "high")
  • Establish appropriate membership functions (triangular, trapezoidal, Gaussian) based on data distribution
  • Calibrate membership function parameters using expert knowledge and historical data

• Fuzzy Rule Base Construction

  • Develop IF-THEN rules relating input and output variables
  • Incorporate expert operator knowledge through structured interviews
  • Validate rule completeness and consistency

• Inference System Implementation

  • Select appropriate inference mechanism (Mamdani or Takagi-Sugeno)
  • Implement fuzzy operators (AND, OR, NOT)
  • Determine aggregation and composition methods

• Model Validation

  • Compare model predictions with actual operational data
  • Perform sensitivity analysis on key parameters
  • Validate model robustness under different data scarcity scenarios

Application Case Study: Stabilization Column Control

Implementation Protocol

Based on research by [1], this protocol details the application of FMCDM for stabilization column control under data scarcity conditions.

Background: Stabilization columns in crude distillation units separate light hydrocarbons from the crude oil mixture. Control is challenging due to varying feed composition and incomplete product quality measurements.

Experimental Workflow:

Step-by-Step Procedure:

• System Identification

  • Identify key control variables: reflux flow, reboiler temperature, column pressure
  • Identify disturbance variables: feed flow rate, feed composition
  • Define performance criteria: product quality, energy efficiency, operational stability

• Fuzzy Model Development

  • Define membership functions for each variable based on historical data and expert knowledge
  • Develop rule base incorporating operator experience
  • Implement fuzzy inference system for parameter prediction

• Multi-Criteria Optimization

  • Apply heuristic method based on main criterion and maximin principle
  • Evaluate solutions against multiple competing objectives
  • Select optimal operating parameters satisfying all constraints

• Implementation and Validation

  • Implement control parameters in simulation environment
  • Validate performance against historical data
  • Refine model based on validation results

Performance Metrics and Results

Table 1: Performance Comparison of Fuzzy vs Traditional Methods for Stabilization Column Control

Metric	Traditional Crisp Model	Fuzzy MCDM Approach	Improvement
Model Accuracy with 20% Missing Data	72.4%	89.6%	+17.2%
Control Stability (Variance)	4.32	2.15	-50.2%
Energy Consumption (Relative)	1.00	0.87	-13.0%
Product Quality Compliance	84.7%	94.2%	+9.5%
Computational Time (Relative)	1.00	1.35	+35.0%

Advanced Techniques for Severe Data Scarcity

Neural Network Integration for Missing Data Prediction

Recent advances in neural network applications to oil and gas infrastructure provide promising approaches for handling severe data scarcity. [44] presents a Bayesian regularization-based neural network framework capable of predicting pipeline life even with missing input parameters.

Implementation Protocol:

• Network Architecture Design

  • Implement feedforward network with Bayesian regularization
  • Determine optimal hidden layer size through cross-validation
  • Initialize weights using Nguyen-Widrow method

• Training with Incomplete Data

  • Use multiple imputation techniques for handling missing values during training
  • Implement dropout regularization to prevent overfitting
  • Apply Bayesian regularization to balance model complexity and fit

• Model Validation

  • Perform k-fold cross-validation with artificially introduced missing data
  • Compare prediction accuracy with traditional methods
  • Validate model robustness through sensitivity analysis

Table 2: Neural Network Performance with Missing Input Parameters [44]

Missing Data Scenario	MSE (Traditional)	MSE (Neural Network)	R² Value
Complete Dataset	0.0245	0.0112	0.963
10% Missing Random	0.0387	0.0156	0.941
25% Missing Random	0.0674	0.0243	0.902
Critical Parameter Missing	0.142	0.0389	0.861

Type-2 Fuzzy Logic for Enhanced Uncertainty Handling

For applications with significant uncertainty in measurements, Type-2 Fuzzy Inference Systems provide enhanced capability for handling uncertainty. [45] demonstrates successful application of Mamdani Type-2 fuzzy logic for well selection in gas lift operations, managing imprecision in key production parameters.

Implementation Workflow:

• Footprint of Uncertainty Modeling

  • Define upper and lower membership functions for critical parameters
  • Model uncertainty in measurements and expert judgments
  • Implement type-reduction algorithms

• Inference with Uncertain Data

  • Develop rules accommodating parameter uncertainty
  • Implement type-2 fuzzy inference mechanism
  • Apply Karnik-Mendel algorithm for type-reduction

The Researcher's Toolkit

Table 3: Essential Research Reagents and Computational Tools for FMCDM in Refinery Applications

Tool/Reagent	Specification/Purpose	Application Context
Fuzzy Logic Toolbox	MATLAB R2020a+	Development and simulation of fuzzy inference systems
scikit-fuzzy	Python 3.7+	Open-source fuzzy logic implementation
Triangular Fuzzy Numbers	(a, b, c) representation	Modeling uncertain parameters with known min, max, most likely values
Unsymmetrical Triangular Fuzzy Numbers	(a, b, c, d) representation	Modeling skewed uncertainty distributions [46]
Neural Network Framework	PyTorch 1.8+ / TensorFlow 2.4+	Implementing Bayesian regularized networks for missing data
Process Simulator	Aspen HYSYS / ChemCAD	Validation of control strategies under uncertainty
API Gravity Analyzer	ASTM D287 standard	Crude oil characterization for feedstock uncertainty modeling [47]
Membership Function Designer	Custom graphical tool	Visual design and tuning of membership functions

Validation and Compliance Protocol

Model Validation Under Data Scarcity Conditions

Objective: Validate fuzzy multi-criteria decision-making models under various data scarcity scenarios.

Procedure:

• Controlled Data Elimination
  • Systematically remove portions of dataset (10%, 25%, 50%)
  • Evaluate model performance degradation compared to traditional methods
  • Assess robustness through multiple random elimination patterns

• Cross-Validation

  • Implement k-fold cross-validation with artificial data gaps
  • Compare prediction accuracy across different uncertainty levels
  • Validate statistical significance of performance differences

• Industrial Case Validation

  • Apply to historical refinery data with documented operational issues
  • Compare model recommendations with actual operator actions
  • Quantify potential improvements through back-testing

Performance Metrics and Success Criteria

Primary Metrics:

• Prediction Accuracy: Mean Absolute Percentage Error (MAPE) under data scarcity
• Robustness: Performance degradation rate with increasing missing data
• Computational Efficiency: Solution time relative to problem complexity
• Implementation Success: Rate of successful field implementations

This application note has detailed methodologies and protocols for addressing data scarcity and incomplete information in refinery models using fuzzy multi-criteria decision-making approaches. The implemented frameworks demonstrate significant advantages over traditional crisp modeling methods, particularly in scenarios with missing parameters and uncertain measurements. Through the integration of fuzzy logic, neural networks, and multi-criteria optimization techniques, refinery researchers and engineers can develop more robust and adequate models that maximize the utility of available information while explicitly accounting for data limitations. The provided protocols enable systematic implementation and validation of these approaches across various refinery applications, from stabilization column control to equipment life prediction.

The control of oil-refining units represents a classic challenge in industrial process optimization, where the imperative for operational efficiency often directly conflicts with environmental impact goals. Traditional optimization methods, which treat these objectives as crisp, well-defined targets, frequently fail to capture the inherent uncertainties and subjective judgments present in real-world refinery operations. This application note frames this balancing challenge within the theoretical framework of fuzzy multi-criteria decision-making (FMCDM), which provides a mathematical foundation for handling imprecise information and conflicting objectives simultaneously [1]. We present structured protocols and data to enable researchers to apply FMCDM principles to refinery control systems, particularly the stabilization column and other key units, where parameters must be optimized across both economic and environmental dimensions.

Theoretical Framework: Fuzzy Multi-Criteria Decision Making

In the context of oil-refining control, "fuzziness" arises from several sources: vague linguistic descriptions from operators (e.g., "high" temperature, "acceptable" emission level), uncertain measurement data, and fluctuating economic and environmental constraints. Fuzzy set theory allows these ambiguous parameters to be represented as membership functions rather than crisp values [1].

The multi-criteria decision problem can be formalized as:

• Objective 1: Maximize Operational Efficiency (e.g., yield, throughput)
• Objective 2: Minimize Environmental Impact (e.g., energy consumption, emissions)

These objectives are inherently conflicting. For instance, maximizing throughput in a distillation column often requires higher energy input, thereby increasing the carbon footprint. FMCDM methods, such as those based on the maximin principle and the main criterion method, allow for the iterative identification of a compromise solution that satisfies both objectives to a satisfactory degree, leveraging the knowledge and preference of the decision-maker (DM) [1].

The following diagram illustrates the core logical workflow of the FMCDM process for refinery control.

Quantitative Data and Performance Benchmarks

Effective decision-making requires a clear understanding of the quantitative trade-offs between operational and environmental performance. The data below, synthesized from current industry analyses, provides key benchmarks for evaluating FMCDM outcomes.

Table 1: Key Performance Indicators and Benchmarks for Refinery Optimization

Performance Category	Specific Metric	Current Industry Benchmark / Target	Potential Improvement via Optimization	Primary Trade-off
Operational Efficiency	Cost Savings from Comprehensive Transformation	Up to $3 per barrel of input crude [16]	Foundational for competitiveness	Requires upfront investment
	Refining Margin Pressure	Downstream earnings ~60% lower in 2024 vs. 2022 [16]	Mitigation via cost control	N/A
	Personnel & Maintenance Productivity	Maintenance productivity <30% (vs. 65% world-class) [16]	>100% improvement potential	Requires organizational change
Environmental Impact	Energy Performance Savings	$0.30 – $0.90 per barrel [16]	5-15% of total cost savings	Lower immediate ROI
	Data Center Power Demand (Indirect Impact)	~3 Bcf/d new natural gas demand by 2030 [48]	Increases operational cost pressure	N/A
Technology Enablers	AI/Advanced Analytics Cost Reduction	$0.40 – $1.45 per barrel of crude [16]	Significant margin preservation	High implementation failure rate

Table 2: FMCDM Experimental Input Parameters for a Stabilization Column

Parameter Type	Parameter Name	Description	Fuzzy Representation (Example)	Data Source
Control Variable	Reflux Ratio	Ratio of liquid returned to the column vs. product draw	Linguistic: "Low", "Optimal", "High"	Fuzzy model [1]
Control Variable	Boil-up Rate	Vapor generated in the reboiler	Linguistic: "Low", "Optimal", "High"	Fuzzy model [1]
Operational Objective	Product Yield	Amount of on-spec product per unit crude	Maximize (Membership: 0-1)	Crude Oil Yield Estimation [49]
Environmental Objective	Specific Energy Consumption	Energy used per unit of product	Minimize (Membership: 0-1)	Simulation-Based Optimization [50]
Constraint	Emission Limit	Maximum allowable CO2/SOx	Fuzzy threshold with tolerance	ENERGY STAR Guidelines [51]

Experimental Protocols for FMCDM in Refinery Control

Protocol: Development of a Fuzzy Model for Process Control

Objective: To create a fuzzy model of a refining unit (e.g., stabilization column) that captures system behavior using expert knowledge and operational data for subsequent FMCDM [1].

• System Scoping and Data Acquisition:

  • Define the boundaries of the target system (e.g., stabilization column including reboiler, condenser, and associated trays).
  • Collect historical operational data, including input parameters (e.g., feed temperature, reflux rate) and output parameters (e.g., product quality, energy consumption).
  • Conduct expert interviews with process engineers and operators to gather linguistic rules describing system behavior and control actions.

• Fuzzification of Input and Output Variables:

  • Select key process variables to be modeled as fuzzy sets (e.g., temperature, pressure, flow rates).
  • For each variable, define 3-5 linguistic terms (e.g., Low, Medium, High) and assign appropriate membership functions (e.g., triangular, trapezoidal). The shape and overlap of these functions should reflect expert judgment and data distribution.

• Fuzzy Rule Base Construction:

  • Formulate IF-THEN rules that map relationships between fuzzy inputs and outputs. Example: "IF Temperature is High AND Pressure is Medium, THEN Product Purity is High."
  • The rule base should be comprehensive, covering all expected operational scenarios, and can be built from expert knowledge, or extracted from data using machine learning techniques.

• Model Validation and Calibration:

  • Test the fuzzy model's predictions against a reserved portion of historical data not used in development.
  • Compare model outputs to known results and adjust membership functions and rules iteratively to minimize error.
  • The model is judged effective when it adequately represents the system's behavior under the collected fuzzy information [1].

Protocol: Multi-Criteria Optimization of Operating Parameters

Objective: To determine the optimal operating point for a refining unit that balances conflicting objectives using an FMCDM heuristic [1].

• Problem Formulation:

  • Define the set of decision variables (e.g., reflux ratio, reboiler duty).
  • Formulate the multiple, conflicting objective functions (e.g., f1(x): Maximize Yield; f2(x): Minimize Energy Consumption).
  • Define all relevant constraints (e.g., product quality specifications, equipment operating limits) as fuzzy sets.

• Application of FMCDM Heuristic:

  • Step 1: Select a primary objective (e.g., "Ensure product yield is at least High").
  • Step 2: Formulate the remaining objectives as flexible constraints using the maximin principle. This principle aims to maximize the minimum satisfaction level across all objectives, ensuring no single objective is poorly met [1].
  • Step 3: Solve the resulting single-criterion problem iteratively, engaging the DM to refine preferences after each solution is presented.

• Solution Validation and Implementation:

  • Validate the compromise solution through process simulation software before implementing it in the actual control system [49].
  • Implement the optimized setpoints in the refinery's Distributed Control System (DCS).
  • Monitor key performance indicators (KPIs) from Table 1 to verify that both operational and environmental goals are being met at the predicted levels.

Protocol: Simulation-Based Optimization with Knowledge Discovery

Objective: To use discrete-event simulation and data mining to identify rules for achieving targeted performance levels in energy efficiency and productivity [50].

• System Modeling and Simulation:

  • Develop a high-fidelity simulation model of the production line or refining unit, incorporating logic for material flow, energy consumption, and queueing.
  • Run the simulation under a wide range of input parameters to generate a comprehensive dataset of operational scenarios and their outcomes.

• Multi-Objective Optimization:

  • Connect the simulation model to an optimization algorithm (e.g., a multi-objective evolutionary algorithm).
  • Execute the optimization to find the Pareto-optimal set of solutions that represent the best trade-offs between energy efficiency and productivity [50].

• Knowledge Discovery via Data Mining:

  • Apply data mining techniques (e.g., decision tree learning, association rule mining) to the Pareto-optimal solution set.
  • Extract actionable, human-readable "rules" that describe the combinations of parameters necessary to achieve specific performance targets (e.g., "IF inventory_level is X AND machine_speed is Y, THEN specific_energy_consumption < Z").

The Researcher's Toolkit

Table 3: Essential Research Reagents and Computational Tools

Item Name	Type/Source	Function in FMCDM Research
Process Simulation Software	Commercial (Aspen HYSYS, ChemCAD)	Creates a digital twin of the refining unit for safe testing and validation of fuzzy control strategies without disrupting live operations [49].
Data Analytics & AI Platform	Open Source (Python, R) or Commercial	Used for developing and training fuzzy models, running optimization algorithms, and performing the knowledge discovery step from simulation data [50] [16].
Fuzzy Logic Toolbox	Open Source (e.g., SciKit-Fuzzy)	Provides pre-built functions for creating fuzzy sets, membership functions, and inference systems, accelerating the development of the core FMCDM model.
Multi-Objective Evolutionary Algorithm (MOEA)	Open Source (e.g., DEAP, pymoo)	Used to approximate the Pareto-optimal frontier in simulation-based optimization, identifying the set of non-dominated solutions for subsequent analysis [50].
ENERGY STAR Guidelines	U.S. Environmental Protection Agency	Provides a standard framework for benchmarking energy performance and identifying improvement opportunities, serving as a key source for environmental criteria and benchmarks [51].
Solomon Associates EII	Solomon Associates	An industry-standard Energy Intensity Index used to benchmark a refinery's energy performance against its peers, providing a crisp metric that can be fuzzified for inclusion in FMCDM [51].

Integrated Workflow and Signaling Pathway

The following diagram synthesizes the protocols and tools into a cohesive, iterative workflow for managing conflicting objectives in refinery control. It highlights the central role of FMCDM in integrating data, models, and human expertise.

Strategies for Determining Optimal Criteria Weights Under Uncertainty

In the complex and data-sensitive environment of oil-refining unit control, Multi-Criteria Decision-Making (MCDM) is essential for optimizing operational parameters that often conflict, such as throughput, energy consumption, product quality, and environmental compliance. The accuracy of these decisions hinges critically on assigning appropriate weights to the various criteria, a task complicated by significant data uncertainty, subjective expert judgments, and imprecise process measurements. Fuzzy set theory provides a robust mathematical foundation for quantifying and managing these uncertainties. This document outlines structured strategies and detailed protocols for determining optimal criteria weights under uncertainty, tailored specifically for research applications in oil-refining control systems. The subsequent sections present a comparative analysis of established weighting methods, detailed experimental protocols for their application, and visualized workflows to guide researchers and scientists in implementing these techniques effectively.

Comparative Analysis of Fuzzy Weighting Methods

Selecting an appropriate weighting method is a foundational step in fuzzy MCDM. Different methods are suited to different types of problems and available data. The table below summarizes the key characteristics of prominent fuzzy weighting methods, providing a guide for selection within oil and gas research contexts.

Table 1: Comparison of Fuzzy Multi-Criteria Weighting Methods

Method Name	Underlying Principle	Data Input Requirements	Key Strengths	Key Limitations	Suitability for Oil & Gas Research
Fuzzy Analytic Hierarchy Process (FAHP)	Pairwise comparisons of criteria based on expert judgment using fuzzy scales [40] [52].	Expert opinions on the relative importance of all possible criterion pairs.	Captures expert knowledge and experience; handles subjectivity and consistency [53].	Prone to biases; consistency of judgments must be verified; can be time-consuming for many criteria.	High suitability for problems with strong reliance on expert knowledge, such as safety risk assessment or strategic planning [54] [55].
CRITIC (Criteria Importance Through Intercriteria Correlation)	Objective weights based on the contrast intensity and conflicting nature between criteria [40] [7].	Performance data of alternatives across all criteria (e.g., historical process data).	Objective and data-driven; avoids expert bias; incorporates correlation structure [40].	Requires reliable and sufficient quantitative data; ignores decision-maker preferences.	Ideal for data-rich environments like process optimization where historical operational data is available.
Entropy-Based Weighting	Measures the amount of information (uncertainty) contained in the evaluation data for each criterion.	Performance data of alternatives across all criteria.	Purely objective method; mathematically straightforward calculation.	Can produce counter-intuitive weights if data is noisy; does not incorporate preferences.	Suitable for initial, data-driven weight estimation in technical performance evaluations.
Rankability-Based Weighting	A spectral graph-based method that analyzes the dominance relationships and structure within the evaluation data [6].	Performance data of alternatives across all criteria.	Overcomes limitations of entropy method; considers multiple evaluation factors and dominance [6].	A newer, less established method; can be computationally more complex.	Promising for complex decisions with many alternatives, such as supplier selection or technology screening [6].
Fuzzy Direct Weighting	Experts assign importance weights to criteria directly using linguistic terms converted to fuzzy numbers.	Expert opinions on the absolute importance of each criterion.	Simple and fast; minimal cognitive load on experts.	Can be less precise than pairwise methods like AHP; does not check for consistency.	Useful for preliminary studies or when a large number of criteria makes pairwise comparisons impractical.

Detailed Experimental Protocols for Weight Determination

This section provides step-by-step protocols for implementing two of the most prevalent and complementary weighting methods in fuzzy MCDM: the subjective Fuzzy AHP and the objective CRITIC method.

Protocol 1: Fuzzy Analytic Hierarchy Process (FAHP)

The FAHP protocol is designed to systematically translate expert linguistic judgments into reliable criterion weights.

1. Research Reagent Solutions

Table 2: Essential Materials for FAHP Protocol

Item Name	Specifications / Function
Expert Panel	5-10 domain experts (e.g., process engineers, control system specialists, operations managers).
Linguistic Scale	A predefined set of terms (e.g., "Equally Important", "Weakly More Important", "Strongly More Important") and their corresponding Triangular Fuzzy Numbers (TFNs), e.g., (1, 1, 1) for "Equally Important" and (2, 3, 4) for "Weakly More Important" [40].
Fuzzy Pairwise Comparison Matrix (~A)	An n x n matrix, where n is the number of criteria. Each element ã_ij is a TFN representing the fuzzy comparison of criterion i to j [40].
Software Tool	Mathematical computing environment (e.g., MATLAB, Python with NumPy/SciPy) for handling fuzzy arithmetic operations.

2. Step-by-Step Procedure

• Define the Criteria Hierarchy: Establish a clear hierarchy of the decision problem, with the overall goal at the top, followed by criteria and sub-criteria. For oil-refining control, top-level criteria may include Operational Cost, Product Yield, Equipment Safety, and Environmental Impact.
• Elicit Expert Judgments: For each pair of criteria at the same hierarchical level, each expert provides a linguistic judgment on their relative importance.
• Construct Fuzzy Pairwise Matrices: Aggregate individual expert judgments (e.g., by taking the geometric mean) to build a consolidated fuzzy pairwise comparison matrix Ã for the group.
• Check Consistency: a. Defuzzify: Convert the fuzzy matrix Ã to a crisp matrix using a method like the Centroid method. b. Calculate Consistency Index (CI): CI = (λ_max - n) / (n - 1), where λ_max is the principal eigenvalue. c. Verify Ratio: Ensure the Consistency Ratio (CR = CI / RI, where RI is the Random Index) is < 0.10. If not, return to Step 2 for expert re-evaluation.
• Compute Fuzzy Weights: Apply the geometric mean method to the fuzzy matrix Ã to calculate the fuzzy weight for each criterion. For criterion i, the fuzzy geometric mean is calculated as: r̃_i = ( ∏_{j=1}^n ã_ij )^(1/n) The fuzzy weight is then: w̃_i = r̃_i ⊗ ( r̃_1 ⊕ r̃_2 ⊕ ... ⊕ r̃_n )^(-1)
• Defuzzify Fuzzy Weights: Convert the resulting fuzzy weights (l, m, u) into crisp weights w_i using a method such as the Centre of Area (COA): w_i = (l + m + u) / 3.
• Normalize Weights: Normalize the crisp weights so that they sum to 1: Normalized w_i = w_i / ∑ w_i.

Protocol 2: Fuzzy CRITIC Method

The Fuzzy CRITIC protocol is used to derive objective weights based on the data matrix of alternative performances, effectively handling uncertainty in measured or predicted values.

1. Research Reagent Solutions

Table 3: Essential Materials for Fuzzy CRITIC Protocol

Item Name	Specifications / Function
Performance Data Matrix	A matrix where rows are alternatives (e.g., different control strategies) and columns are criteria. Each cell is a fuzzy number (e.g., TFN) representing the performance score.
Fuzzy Normalization Scheme	Formulas to transform fuzzy scores of different units and scales (beneficial vs. cost criteria) into dimensionless, comparable values [7].
Correlation Calculator	Algorithm to compute the correlation coefficient between columns of the normalized fuzzy decision matrix.
Software Tool	Mathematical computing environment capable of fuzzy arithmetic and matrix operations.

2. Step-by-Step Procedure

• Construct the Fuzzy Decision Matrix (Ẋ): Build an m x n matrix where m is the number of alternatives and n is the number of criteria. Each element x̃_ij is a fuzzy number (e.g., TFN) denoting the performance of alternative i under criterion j.
• Normalize the Fuzzy Decision Matrix (Ŕ):
  • For beneficial criteria (higher is better): r̃_ij = ( x̃_ij - min(x̃_j) ) / ( max(x̃_j) - min(x̃_j) )
  • For cost criteria (lower is better): r̃_ij = ( max(x̃_j) - x̃_ij ) / ( max(x̃_j) - min(x̃_j) )
  • Note: Fuzzy arithmetic operations are used.
• Calculate the Standard Deviation (σ̃_j): Compute the fuzzy standard deviation for each criterion j across all alternatives. This measures the contrast intensity of that criterion.
• Compute the Fuzzy Correlation Coefficient (ρ̃_jk): Calculate the fuzzy correlation between each pair of criteria (j, k). This quantifies the conflict between criteria.
• Calculate the Information Measure (C̃_j): For each criterion j, compute: C̃_j = σ̃_j ⊗ ∑_{k=1}^n ( 1 - ρ̃_jk ) This combines contrast intensity and conflict.
• Determine the Objective Weights: Defuzzify each C̃_j to a crisp value C_j. The objective weight for criterion j is then: w_j = C_j / ∑_{k=1}^n C_k

Integrated Weighting and Advanced Strategies

For comprehensive decision-making, a hybrid approach that combines subjective and objective weighting is often most robust. Furthermore, advanced fuzzy sets can be employed to handle more complex forms of uncertainty.

Hybrid Subjective-Objective Weighting

A linear combination can integrate weights from FAHP (w_j_subj) and Fuzzy CRITIC (w_j_obj) to produce a final weight that reflects both expert preference and data-driven insight: w_j_combined = α * w_j_subj + (1 - α) * w_j_obj where α (0 ≤ α ≤ 1) is an aggregation parameter that can be adjusted based on the decision context and the relative reliability of expert judgment versus available data [40].

Advanced Fuzzy Sets for Complex Uncertainty

When uncertainty cannot be adequately captured by standard triangular fuzzy numbers, more advanced fuzzy sets are available.

• Type-2 Fuzzy Sets: These are used to handle higher-order uncertainty, such as when the membership function itself is uncertain. This is applicable in highly volatile environments or when expert opinions vary significantly [26] [53].
• Spherical Fuzzy Sets (SFS) and t-Spherical Fuzzy Sets (t-SFS): These extend the representation of uncertainty by independently considering membership, non-membership, and hesitancy degrees, offering greater flexibility for modeling expert judgments [7].
• Fractional Fuzzy Sets: A recent innovation that provides even more nuanced control over membership grades, allowing for the handling of specific datasets that traditional models cannot accommodate [7].

Heuristic Methods for Iterative Improvement of Decision-Making in a Fuzzy Environment

The control of complex technological systems, such as those found in the oil-refining industry, is often characterized by non-formalizable parameters and fuzzy initial information. This complicates the development of mathematical models and the optimization of operational modes [1]. Fuzzy multi-criteria decision-making (FMCDM) approaches are particularly suited to these environments, as they incorporate the knowledge and experience of a decision-maker (DM) to manage conflicting criteria where control objectives and constraints are often described in natural language [1]. This document outlines application notes and detailed protocols for employing heuristic FMCDM methods, specifically framed within the context of controlling a Primary Oil-Refining Unit, to enable adequate and effective decision-making that maximizes the use of collected fuzzy information.

Theoretical Foundations and Application Principles

The developed heuristic methods are founded on the modification and combination of different principles of optimality, such as the main criterion and maximin methods [1]. Unlike approaches that convert a fuzzy problem into a set of crisp problems using α-level sets—a process that can lead to the loss of original fuzzy information—the proposed methods operate directly within the fuzzy environment. This allows for iterative improvement and more adequate decision-making by leveraging system models, knowledge, and DM experience [1]. The core advantage of these methods is their ability to handle the fuzziness inherent in complex production facilities without sacrificing the integrity of the original information.

Table 1: Core Components of the Proposed FMCDM Framework

Component	Description	Role in Fuzzy Decision-Making
System Models	Statistical and fuzzy models developed from experimental-statistical methods and expert evaluation [1].	Form the foundational representation of the system's behavior under fuzzy conditions.
Decision Maker (DM)	An experienced operator or expert who manages operating modes [1].	Provides preferences and expert judgment to guide the iterative improvement process.
Optimality Principles	Modified versions of principles like the main criterion and maximin [1].	Serve as the logical basis for evaluating and ranking alternatives in a fuzzy environment.
Fuzzy Information	Initial system information that is incomplete, non-formalizable, or described in natural language [1].	The raw input that the methodology is designed to process without significant loss of content.

Application Notes for Stabilization Column Control

The stabilization column in a primary oil-refining unit serves as an ideal use case. The following notes detail the application of the FMCDM methodology to this specific subsystem.

Problem Formulation

The objective is to solve a two-criterion optimization problem for the stabilization column's parameters in a fuzzy environment. The conflicting criteria, which must be reconciled with the involvement of the DM, could include, for example, product quality and energy consumption [1]. The system is characterized by a large number of interconnected parameters whose influence on operating modes is fuzzy.

Developed Models

Based on experimental-statistical methods and expert evaluations, statistical and fuzzy models of the stabilization column are developed. The conditions for judging the fuzzy model's effectiveness are determined and investigated prior to optimization [1].

Solution via Heuristic FMCDM

The proposed heuristic method, based on a combination of the main criterion and maximin, is applied to solve the two-criterion optimization problem. The results confirm the advantages of this method, demonstrating its ability to yield superior outcomes compared to known methods by more fully utilizing the available fuzzy information [1].

Experimental Protocols

Protocol 1: System Modeling and Fuzzy Model Validation

This protocol details the process for developing the fuzzy model of the stabilization column.

• Data and Knowledge Acquisition:
  • Collect historical operational data from the stabilization column.
  • Conduct structured expert evaluations with experienced operators to gather qualitative knowledge on parameter influences and control objectives. This knowledge is often expressed in natural language (e.g., "if pressure is high, then quality is moderately improved").
• Model Development:
  • Employ experimental-statistical methods to develop a baseline statistical model.
  • Formalize the expert knowledge into fuzzy rules and membership functions to construct the fuzzy model.
• Model Effectiveness Validation:
  • Define quantitative conditions for judging the model's effectiveness (e.g., prediction accuracy of key output variables under fuzzy inputs).
  • Test the model against a reserved validation dataset and compare its performance against the crisp statistical model.

Protocol 2: Two-Criterion Fuzzy Optimization

This protocol outlines the steps for performing the core multi-criteria optimization.

• Problem Setup:
  • Define the two conflicting criteria for optimization (e.g., Criterion 1: Maximize Product Purity; Criterion 2: Minimize Energy Input).
  • Establish the fuzzy constraints and feasible domain for the operating parameters based on the developed fuzzy model.
• Heuristic Method Application:
  • Main Criterion Phase: Select one criterion as the primary objective (e.g., Product Purity). The DM defines an acceptable satisfaction level for the secondary criterion.
  • Maximin Phase: Implement the maximin principle to find a solution that maximizes the minimum satisfaction degree across all criteria, ensuring a balanced compromise.
  • The method iterates between these principles, incorporating DM feedback after each iteration to refine preferences and improve the solution [1].
• Solution Evaluation:
  • Compare the final solution obtained from the proposed heuristic method with solutions from traditional methods (e.g., those based on α-level set conversion).
  • Evaluate performance based on practical implementation results and alignment with expert DM judgment.

Workflow and System Visualization

The following diagram illustrates the logical workflow of the proposed heuristic FMCDM method for controlling the oil-refining unit.

The Scientist's Toolkit: Research Reagent Solutions

Table 2: Essential Materials and Analytical Tools for FMCDM Research

Item	Function / Application
Expert Panel	A group of experienced operators and engineers who provide the qualitative, fuzzy knowledge essential for building the fuzzy rule base and validating decisions [1].
Historical Process Data	Time-series data of operational parameters (temperatures, pressures, flow rates) and product quality measures from the stabilization column. Serves as the foundation for statistical model development [1].
Fuzzy Logic Development Environment	Software tools (e.g., MATLAB Fuzzy Logic Toolbox, Python libraries like scikit-fuzzy) for constructing, simulating, and testing fuzzy inference systems.
Multi-Criteria Decision Analysis (MCDA) Software	Platforms that support the implementation of various optimality principles (maximin, Pareto optimization) for evaluating alternatives against multiple criteria.
Data Visualization & Dashboard Tools	Applications like Power BI or custom dashboards to create clear, interactive visualizations of key performance metrics, trends, and optimization results for effective DM interpretation [56].

Managing Subjectivity and Bias in Expert Evaluations for Refinery Processes

In refinery processes, expert evaluations are essential for optimizing complex operations such as controlling a primary oil-refining unit or selecting non-destructive testing (NDT) techniques. However, these decisions are often plagued by subjectivity and bias arising from vague information, conflicting criteria, and human cognitive limitations [1]. Fuzzy Multi-Criteria Decision-Making (FMCDM) provides a robust mathematical framework to manage this uncertainty and imprecision, translating qualitative expert judgments into quantitative models that minimize bias while systematically incorporating expert knowledge [1] [40].

This document outlines detailed application notes and protocols for implementing FMCDM in refinery contexts, enabling more objective, reliable, and transparent decision-making.

Background and Key Concepts

The Nature of Subjectivity in Refinery Decisions

Refinery processes, including the control of a stabilization column, are characterized by a large number of interconnected parameters whose influence on operating modes and product quality is often non-formalizable and fuzzy [1]. Traditional crisp decision models force experts into artificial precision, potentially discarding valuable nuanced knowledge. Fuzzy set theory, introduced by Zadeh, addresses this by representing uncertain information through membership functions [7].

Fuzzy Sets for Handling Uncertainty

Fuzzy logic extends classical set theory by allowing gradual membership transitions, represented by membership values between 0 and 1. Several advanced fuzzy set types have been developed to capture complex uncertainty, which is common in refinery process data and expert ratings [7].

Table: Types of Fuzzy Sets for Expert Evaluations

Fuzzy Set Type	Key Parameters	Application Context in Refining
Triangular Fuzzy Number (TFN) [40] [57]	Lower bound, Modal value, Upper bound (a₁, a₂, a₃)	Capturing simple vagueness in expert estimates (e.g., "the expected temperature is between 300 and 350°C, most likely 325°C").
Intuitionistic Fuzzy Set (IFS) [57]	Membership degree (MB), Non-membership degree (NMB)	Handling expert hesitancy; useful when an expert is 70% sure an adjustment will work but 20% unsure.
Spherical Fuzzy Set (SFS) [2]	Membership (MB), Non-membership (NMB), Indeterminacy (ID)	Simultaneously modeling approval, disapproval, and abstention in group expert decisions for refinery control.
f, g, h-Fractional Fuzzy Set [7]	Parameters f, g, h to control membership powers	Providing maximum flexibility to handle extreme or complex uncertainties where traditional sets fail.

Application Notes: FMCDM Framework for Refinery Processes

The following framework is adapted from proven applications in oil-refining unit control, NDT technique selection, and crude oil pretreatment [1] [40] [2].

Structured Workflow for Bias-Reduced Decisions

The diagram below illustrates a generalized FMCDM workflow for managing subjectivity and bias in refinery process evaluations.

Quantitative Data from Case Applications

Table: Consolidated Criteria Weights from FMCDM Case Studies in Oil & Gas

Application Domain	Most Influential Technical Criterion (Weight)	Most Influential Economic Criterion (Weight)	Top-Ranked Alternative	Primary FMCDM Method Used
NDT Technique Selection [40]	Spatial Resolution (0.175)	Downtime Costs (0.210)	Radiographic Testing (0.665)	FAHP, TOPSIS, VIKOR, PROMETHEE
Crude Oil Pretreatment [2]	Impurity Removal Efficiency	Operational Energy Cost	Advanced Membrane Filtration	D-SFS, MEREC, SWARA, MARCOS
Oil Refining Unit Control [1]	Product Quality, Throughput	N/A	Optimized setpoints via maximin principle	Fuzzy Heuristic Method

Experimental Protocols

Protocol 1: Fuzzy AHP for Criteria Weighting in Stabilization Column Control

This protocol details the methodology for determining the relative importance of control parameters for a primary oil-refining stabilization column, minimizing subjectivity in expert weighting [1] [40].

Objective: To establish objective weights for conflicting control criteria (e.g., product purity, energy consumption, throughput) using Fuzzy AHP (FAHP). Materials: Expert panel, fuzzy linguistic scale (e.g., Triangular Fuzzy Numbers for "Equally Important" to "Extremely More Important").

Procedure:

• Structure the Hierarchy: Define the goal (e.g., "Optimal Stabilization Column Control"), list relevant criteria (C1, C2,...Cn), and identify potential control alternatives.
• Collect Fuzzy Pairwise Comparisons: Each expert performs pairwise comparisons of criteria using a predefined fuzzy linguistic scale. This captures the vagueness in statements like "Criterion A is moderately more important than Criterion B."
• Construct Fuzzy Judgment Matrices: For each expert k, a fuzzy positive reciprocal matrix Ã^(k) = [ãᵢⱼ] is built, where ãᵢⱼ is a TFN representing the fuzzy comparison between criterion i and j.
• Check Consistency: Calculate the consistency ratio of the defuzzified matrix. If the ratio exceeds 0.10, the expert is asked to revise their judgments.
• Aggregate Expert Judgments: Use a fuzzy geometric mean or similar operator to synthesize individual fuzzy matrices into a consolidated group fuzzy judgment matrix.
• Calculate Fuzzy Weights: Apply the fuzzy extent analysis method to the aggregated matrix to compute the fuzzy weight for each criterion.
• Defuzzify and Normalize: Convert the fuzzy weights into crisp, normalized final weights using a centroid method. The sum of all weights must equal 1.

Protocol 2: f,g,h-Fractional Fuzzy CRITIC-TOPSIS for Evaluating Control Strategies

This advanced protocol uses fractional fuzzy sets to maximize the use of collected fuzzy information and an objective weighting method (CRITIC) to further reduce expert bias [7].

Objective: To rank different operating mode strategies for a refinery unit by leveraging the f,g,h-Fractional Fuzzy CRITIC-TOPSIS method. Materials: Dataset of alternative performance across multiple criteria, structured in an f,g,h-FrFS format.

Procedure:

• Construct the Fractional Fuzzy Decision Matrix: Suppose m control alternatives (A₁, A₂, ..., Aₘ) are evaluated against n criteria (C₁, C₂, ..., Cₙ). The performance rating of alternative i on criterion j is expressed as an f,g,h-FrFS: xᵢⱼ = (MBᵢⱼ, IDᵢⱼ, NMBᵢⱼ), where MB, ID, and NMB are the membership, indeterminacy, and non-membership degrees, respectively.
• Determine Criteria Weights with CRITIC: Calculate objective weights for each criterion based on the contrast intensity of the data.
  • Normalize the fractional fuzzy decision matrix.
  • Compute the standard deviation for each criterion.
  • Calculate the correlation coefficient between all pairs of criteria.
  • Determine the amount of information Cⱼ for each criterion: Cⱼ = σⱼ * ∑ₖ (1 - rⱼₖ), where σⱼ is the standard deviation and rⱼₖ is the correlation coefficient.
  • The objective weight for criterion j is: wⱼ = Cⱼ / ∑ⱼ Cⱼ.
• Identify Ideal and Anti-Ideal Solutions: Determine the f,g,h-FrF positive ideal solution A⁺ and negative ideal solution A⁻.
• Calculate Separation Measures: For each alternative, compute the distance dᵢ⁺ from A⁺ and dᵢ⁻ from A⁻ using the proposed fractional fuzzy Hamming distance.
• Calculate Relative Closeness and Rank: The relative closeness RCᵢ of each alternative to the ideal solution is RCᵢ = dᵢ⁻ / (dᵢ⁺ + dᵢ⁻). Alternatives are ranked in descending order of RCᵢ.

Protocol 3: Multi-Dimensional Sensitivity Analysis

After ranking alternatives, this protocol assesses the stability of results against variations in criteria weights and expert opinions, which is critical for validating the robustness of the decision against potential biases [58].

Objective: To evaluate the sensitivity of the FMCDM ranking to changes in input parameters and ensure the decision is robust. Materials: Final ranking of alternatives, criteria weights, and the decision matrix.

Procedure:

• Perturbation of Criteria Weights: Systematically vary the weight of the most influential criterion (e.g., reduce its weight by 10%, 20%, etc.), simultaneously adjusting other weights to maintain a sum of 1.
• Submodel Exclusion Analysis: Re-run the FMCDM model by excluding one expert's judgments at a time to check if any single expert's bias unduly drives the final outcome.
• Scenario Analysis: Test the model's performance under different predefined operational scenarios (e.g., "maximize throughput" vs. "maximize efficiency") by changing the underlying criteria weight profile.
• Rank Stability Evaluation: After each perturbation, record the new ranking of alternatives. A robust model will show minimal rank reversal. Tools like the Comprehensive Sensitivity Analysis Method (COMSAM) can be employed for this systematic evaluation [58].

The Scientist's Toolkit: Key Research Reagents & Materials

Table: Essential "Reagents" for FMCDM Experiments in Refinery Research

Item / Conceptual Tool	Function / Explanation	Example Use in Refinery Context
Triangular Fuzzy Number (TFN)	Represent vague expert judgments with a lower bound, most likely value, and upper bound.	Quantifying an expert's opinion that a catalyst's optimal temperature is "around 350°C, between 330 and 370°C" as (330, 350, 370).
Linguistic Scale	A predefined set of fuzzy terms (e.g., "Very Low," "High," "Very High") that experts use for qualitative assessments.	Uniformly capturing expert ratings for the "risk of coking" in a furnace tube across multiple alternatives.
Fuzzy Analytic Hierarchy Process (FAHP)	Determine the relative weights of decision criteria through fuzzy pairwise comparisons, reducing subjectivity in weighting.	Establishing that "product sulfur content" (safety) is more important than "energy cost" (economics) for a specific unit operation.
CRITIC Method	An objective weighting method that uses correlation analysis and standard deviation to determine criteria weights from the data itself.	Objectively finding that "throughput variance" is a key discriminator between control strategies without expert input, minimizing anchoring bias.
TOPSIS / FVIKOR	Ranking methods that evaluate alternatives based on their geometric distance from an ideal solution.	Ranking different non-destructive testing methods by their closeness to the ideal technical and economic performance [40].
Sensitivity Analysis Script (e.g., in Python/R)	Automated code to perturb model parameters and test the robustness of the FMCDM ranking.	Systematically validating that the selected crude oil pretreatment method remains optimal even if capital cost estimates are inaccurate [2].

Validating and Comparing FMCDM Approaches for Industrial Reliability

Fuzzy multi-criteria decision-making (MCDM) has emerged as a critical tool for addressing complex optimization and selection challenges in the oil-refining industry. Processes such as crude oil pretreatment, demulsifier selection, and stabilization column control are characterized by multiple, often conflicting criteria, vague information, and significant operational uncertainties [3] [1]. The Fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) represents a significant advancement over conventional selection methods by systematically incorporating fuzzy logic to handle subjective judgments and data imprecision. This application note provides a detailed comparative analysis and experimental protocols to guide researchers in effectively deploying Fuzzy TOPSIS for oil-refining unit control.

Comparative Analysis: Fuzzy TOPSIS vs. Conventional Methods

The following table summarizes a quantitative and qualitative comparison between Fuzzy TOPSIS and conventional selection methods, based on studies conducted in oil-refining and related domains.

Table 1: Comparative analysis of selection methods

Aspect	Fuzzy TOPSIS	Conventional Methods (e.g., Trial-and-Error, Single-Criterion)
Handling of Uncertainty	Uses linguistic variables and fuzzy numbers (e.g., pentagonal, triangular) to quantify vagueness and imprecision [26] [3].	Relies on crisp, precise data; struggles with subjective or incomplete information [3].
Decision Basis	Multi-criteria approach; ranks alternatives by their simultaneous closeness to an ideal and distance from a negative-ideal solution [59] [3].	Often single-criterion focus (e.g., separation efficiency) or unstructured multi-factor consideration [3].
Computational & Time Efficiency	More efficient than some fuzzy MCDM (e.g., Fuzzy AHP) for large alternative sets; lower computational complexity promotes user experience [59] [60].	Empirical approaches (e.g., bottle tests) are time-consuming, costly, and limited in scope [3].
Rank Reversal	Resistant to rank reversal, producing consistent results [59].	Not typically applicable, as methods often lack a formal ranking structure.
Transparency & Structure	Provides a structured, quantitative, and transparent framework for decision-making [3] [60].	Opaque and highly reliant on individual operator experience, leading to potential bias [3].
Number of Judgments Required	Requires fewer direct pairwise comparisons than methods like Fuzzy AHP [59].	Not formally defined, but repeated physical tests can be numerous and resource-intensive.

Application Protocols for Oil-Refining Unit Control

Protocol 1: Fuzzy TOPSIS for Optimal Demulsifier Selection

Application Objective: To systematically select the most effective chemical demulsifier for crude oil dehydration by evaluating multiple performance criteria under uncertainty [3].

Experimental Workflow:

• Define Alternatives and Criteria: Identify the commercial demulsifiers (e.g., Alcopol 500, Nalco Champion EC7135A) to be evaluated. Establish the evaluation criteria, which typically include:
  • Separation Efficiency: The primary performance metric for water separation.
  • Environmental Impact: Toxicity and ecological footprint of the demulsifier.
  • Cost Effectiveness: Overall cost per unit and treatment cost.
  • Ease of Application: Handling and integration into existing processes [3].
• Assign Weights to Criteria: Determine the importance weight of each criterion, often through expert opinion. Use a linguistic scale (e.g., "Very Low," "Low," "Medium," "High," "Very High") which is then converted into corresponding fuzzy numbers (e.g., triangular fuzzy numbers).
• Rate Alternatives with Linguistic Variables: For each demulsifier alternative, experts evaluate its performance against every criterion using the same linguistic scale. These ratings are also converted into fuzzy numbers, constructing a fuzzy decision matrix.
• Construct the Fuzzy Decision Matrix: Assemble the weights and ratings into a normalized fuzzy decision matrix.
• Execute Fuzzy TOPSIS Calculations:
  • Calculate the Fuzzy Positive Ideal Solution (FPIS) and Fuzzy Negative Ideal Solution (FNIS).
  • Compute the distance of each alternative from the FPIS and FNIS.
  • Calculate the Closeness Coefficient (CC~i~) for each alternative using the formula: CC~i~ = d~i~^-^ / (d~i~^ + d~i~^-^), where *d~i~^-^ is the distance from FNIS and d~i~^ * is the distance from FPIS.
• Rank Alternatives: Rank the demulsifiers in descending order of their Closeness Coefficient. The alternative with the highest CC value (closest to 1) is the most preferred. In a cited study, Nalco Champion EC7135A (CC=0.751) ranked highest, followed by Alcopol 500 (CC=0.708) [3].

The following diagram illustrates the logical workflow for this protocol:

Protocol 2: Conventional Bottle Test Method for Demulsifier Selection

Application Objective: To empirically determine demulsifier efficiency via laboratory bottle tests, a traditional industry approach [3].

Experimental Workflow:

• Sample Preparation: Prepare a series of identical bottles or graduated tubes containing a set volume of the crude oil emulsion.
• Chemical Dosing: Add different demulsifier candidates or varying concentrations of a single demulsifier to each bottle.
• Agitation and Static Settlement: Agitate the bottles thoroughly to mix the demulsifier, then allow them to stand undisturbed at a controlled temperature for a predefined period (e.g., 1-2 hours).
• Data Collection and Analysis: Measure the volume of separated water in each bottle over time. The demulsifier yielding the highest water separation percentage in the shortest time is considered the most effective.
• Drawbacks: This method is time-consuming, requires significant physical materials, and evaluates performance primarily on a single criterion (separation efficiency), potentially overlooking cost, environmental impact, and operational feasibility [3].

Case Study: Stabilization Column Control Optimization

A study on controlling the operating modes of a primary oil-refining stabilization column demonstrated the efficacy of fuzzy MCDM. The column was characterized by fuzzy initial information and non-formalizable parameter influences, making traditional crisp modeling inadequate [1].

Implementation:

• Fuzzy Model Development: Experimental-statistical methods and expert evaluations were used to develop statistical and fuzzy models of the stabilization column.
• Multi-criteria Optimization: A heuristic fuzzy MCDM method, based on the main criterion and maximin principle, was employed for a two-criterion optimization of the column's parameters.
• Outcome: The proposed fuzzy decision-making method provided more adequate and effective control solutions by fully utilizing the available fuzzy information, outperforming the results of known methods that converted the fuzzy problem into a set of crisp problems [1].

The Scientist's Toolkit: Key Research Reagents and Materials

Table 2: Essential materials for fuzzy MCDM experiments in oil refining

Item	Function/Description
Commercial Demulsifiers	Chemical agents (e.g., Alcopol 500, Nalco Champion EC7135A) used as alternatives in dehydration selection studies [3].
Crude Oil Emulsion Samples	Real or synthetic water-in-oil emulsions with characterized properties (e.g., asphaltene, resin, wax content) for experimental testing [3].
Linguistic Variable Set	A predefined scale (e.g., Very Poor, Poor, Fair, Good, Very Good) to facilitate expert qualitative judgments [3] [60].
Fuzzy Number Type	A mathematical representation (e.g., Triangular, Pentagonal) to convert linguistic variables into a computable format for constructing the decision matrix [26] [3].
Process Historian Data	Archived operational data from refinery control systems used to build and validate fuzzy models of units like the stabilization column [61] [1].

Benchmarking Hybrid D-SFS Models Against Established Techniques like CoCoSo

Application Notes: The Role of D-SFS and CoCoSo in Oil-Refining Decision-Making

The complex, multi-faceted nature of oil-refining unit control presents significant decision-making challenges, where parameters are often uncertain, imprecise, and subject to expert interpretation. Disc Spherical Fuzzy Sets (D-SFS) provide a sophisticated mathematical framework for capturing these complex uncertainties. D-SFS extends Spherical Fuzzy Sets by incorporating a circular or disc-based representation of membership, non-membership, and hesitancy degrees, offering a more nuanced way to model expert judgments and ambiguous data prevalent in refinery operations [2]. This enhanced capability is particularly valuable for representing the three-dimensional nature of human assessment in complex refinery control scenarios.

The Combined Compromise Solution (CoCoSo) method is a multi-criteria decision-making (MCDM) technique that integrates multiple compromise solution strategies to rank alternatives robustly. It combines the Simple Additive Weighting (SAW) and Exponentially Weighted Product (EWP) models through three separate aggregation strategies to arrive at a final compromise ranking [62] [63]. This multi-strategy approach enhances ranking reliability—a critical factor when evaluating refinery control strategies where suboptimal decisions carry significant economic and safety consequences.

Practical Application in Petroleum Sector

The integration of D-SFS with MCDM methods demonstrates substantial practical utility in petroleum sector applications. Research has shown that hybrid D-SFS approaches can effectively evaluate crude oil pretreatment techniques—a critical unit operation in refining [2]. These methods systematically balance competing criteria such as separation efficiency, energy consumption, contaminant reduction, and environmental compliance when selecting optimal pretreatment strategies.

For oil-refining unit control specifically, the D-SFS framework enables more faithful representation of expert assessments across multiple performance dimensions. The disc-based model captures the inherent vagueness in operational parameters, while CoCoSo provides a structured methodology to rank control strategies based on their overall performance across technical, economic, and environmental criteria [2] [64]. This combination has proven effective in handling the complex, often conflicting objectives that characterize refinery optimization problems.

Table 1: Fuzzy Set Frameworks for Uncertainty Modeling in Petroleum Applications

Fuzzy Framework	Key Characteristics	Application in Petroleum Sector
Disc Spherical Fuzzy Sets (D-SFS)	Incorporates membership, non-membership, and hesitancy with circular/disc representation	Crude oil pretreatment evaluation; refinery process optimization [2]
Spherical Fuzzy Sets (SFS)	Three-dimensional membership with squared sum constraint ≤ 1	Wave energy converter assessment for offshore operations [65]
(p–q) Rung Orthopair Fuzzy Sets	Broader uncertainty representation space than Pythagorean/ Fermatean sets	Health care waste management selection [66]
Probabilistic Hesitant Fuzzy Sets	Incorporates probability distributions to hesitant assessments	Dynamic plastic product selection [67]

Experimental Protocols

Protocol: Benchmarking D-SFS Against CoCoSo for Refinery Control Optimization

Research Reagents and Computational Tools

Table 2: Essential Research Components for Fuzzy MCDM Implementation

Component/Tool	Function/Purpose	Implementation Notes
Decision Criteria Matrix	Structured representation of alternatives vs. criteria	Forms the foundational data structure for MCDM analysis
Expert Assessment Panel	Provide qualitative judgments on alternatives	Typically 3-5 domain experts with refinery operations experience
Aczel-Alsina Aggregation Operators	Information fusion under D-SFS environment	Particularly effective within D-SFS framework [2]
MEREC (Method based on Removal Effects of Criteria)	Objective criteria weighting	Determines weight based on impact of removing each criterion [2] [65]
SWARA (Step-Wise Weight Assessment Ratio Analysis)	Subjective criteria weighting	Captures expert-driven criterion importance [2]
CoCoSo Algorithm	Alternative ranking and compromise solution	Original or modified version for final ranking [62]
Sensitivity Analysis Framework	Robustness validation of results	Perturbation of weights and parameters to test stability [68]

Methodology

Phase 1: Problem Structuring and Criteria Definition

• Define Refinery Control Alternatives: Identify specific control strategies, technologies, or operational policies to be evaluated (e.g., PID variants, model predictive control, fuzzy logic controllers).
• Establish Evaluation Criteria: Determine technical, economic, and environmental criteria relevant to refinery unit control (e.g., control stability, implementation cost, energy efficiency, emission reduction, scalability).
• Constitute Expert Panel: Engage 3-5 domain experts with substantial experience in refinery operations and process control.

Phase 2: Data Collection and D-SFS Representation

• Expert Assessment Collection: Solicit expert evaluations of each alternative against all criteria using appropriate linguistic scales.
• Transform to D-SFS Format: Convert linguistic assessments into D-SFS representations, capturing membership (μ), non-membership (ν), and hesitancy (π) parameters within the disc-based structure [2].
• Aggregate Expert Opinions: Utilize D-SFS aggregation operators (e.g., Aczel-Alsina weighted averaging) to combine individual expert assessments into a collective evaluation matrix.

Phase 3: Criteria Weight Determination

• Objective Weight Calculation: Apply the MEREC method to determine objective weights based on the decision matrix itself [2] [65].
• Subjective Weight Calculation: Implement SWARA to derive subjective weights through expert pairwise comparisons of criterion importance [2].
• Weight Integration: Compute combined criteria weights through weighted integration of objective and subjective weights.

Phase 4: Alternative Ranking with CoCoSo

• Normalize Decision Matrix: Transform aggregated D-SFS evaluations into normalized values, considering benefit and cost criteria appropriately.
• Calculate Weighted Sums: Compute the weighted sum (Si) and weighted product (Pi) values for each alternative using the normalized matrix and combined weights.
• Apply Three CoCoSo Strategies: Calculate three performance measures for each alternative [62] [63]:
  • Strategy 1: ( k{ia} = \frac{Pi + Si}{\sum{i=1}^{m}(Pi + Si)} )
  • Strategy 2: ( k{ib} = \frac{Si}{\mini Si} + \frac{Pi}{\mini Pi} )
  • Strategy 3: ( k{ic} = \frac{\lambda(Si) + (1-\lambda)(Pi)}{(\lambda \maxi Si + (1-\lambda) \maxi Pi)} ) ( \text{where } 0 \leq \lambda \leq 1 )
• Compute Final Rankings: Calculate final performance scores ( ki = \frac{1}{3}(k{ia} + k{ib} + k{ic}) ) or ( ki = \sqrt[3]{k{ia} \cdot k{ib} \cdot k{ic}} ) and rank alternatives accordingly.

Phase 5: Validation and Sensitivity Analysis

• Comparative Analysis: Compare D-SFS-CoCoSo rankings against other MCDM methods (TOPSIS, VIKOR, EDAS, MARCOS) to identify ranking consistency [68] [2].
• Parameter Sensitivity: Test sensitivity by varying the compromise coefficient (λ) in CoCoSo and observing rank stability [68].
• Weight Perturbation: Systematically alter criteria weights to assess solution robustness under changing preference scenarios.

Protocol: Performance Metrics for Method Comparison

Evaluation Framework Implementation

• Ranking Consistency Measurement:

  • Apply both D-SFS hybrid method and standard CoCoSo to the same refinery control dataset
  • Calculate rank correlation coefficients (Spearman's ρ, Kendall's τ) to quantify similarity
  • Identify and analyze positions where ranking differences occur

• Computational Efficiency Assessment:

  • Measure execution time for both methods across varying problem sizes (number of alternatives, criteria)
  • Document computational resource requirements (memory, processing power)
  • Analyze algorithmic complexity and scalability

• Solution Robustness Evaluation:

  • Implement sensitivity analysis by perturbing input parameters and criteria weights
  • Calculate stability indices based on ranking changes
  • Identify critical criteria that most significantly influence outcomes

• Decision Quality Assessment:

  • Evaluate method performance against historical refinery control decisions
  • Assess alignment with expert consensus on optimal control strategies
  • Measure ability to distinguish between subtly different alternatives

Table 3: D-SFS and CoCoSo Hybridization Approaches in MCDM Literature

Hybrid Approach	Core Methodology	Reported Advantages	Application Domain
D-SFS with MEREC-SWARA-MARCOS	D-SFS with objective-subjective weighting and MARCOS ranking	High reliability and consistency in complex decisions	Crude oil pretreatment [2]
IVSF-CoCoSo	Interval-valued spherical fuzzy sets with CoCoSo	Enhanced expressiveness of uncertainty; stable rankings	Visual communication design tools [68]
SF-CoCoSo with MEREC	Spherical fuzzy sets with CoCoSo and objective weighting	Improved objectivity in uncertainty modeling	Wave energy converter benchmarking [65]
Borda-CoCoSo	CoCoSo enhanced with Borda rule for ranking	Improved group decision consistency	Dynamic plastic products [67]
T-Spherical Fuzzy CoCoSo	T-spherical fuzzy sets with Frank operational laws	Broader expression space; handles risk preference	Battery recycling technology [63]

Comparative Analysis and Implementation Guidelines

Performance Benchmarking Results

Based on comparative studies between hybrid D-SFS models and established CoCoSo implementations, several key findings emerge:

• Ranking Consistency: The D-SFS framework demonstrates 96.43% consistency with expert judgments in complex decision scenarios, outperforming traditional fuzzy approaches in capturing nuanced expert assessments [67].

• Stability Performance: Hybrid D-SFS models exhibit superior stability metrics (0.046 stability index) compared to standalone CoCoSo implementations when dealing with the high-dimensional, uncertain parameters characteristic of refinery control systems [67].

• Uncertainty Handling: The disc-based structure of D-SFS provides more flexible representation of ambiguous refinery operational data compared to conventional fuzzy sets, leading to more reliable decision outcomes in situations with conflicting performance criteria [2] [64].

Implementation Recommendations for Oil-Refining Applications

• Method Selection Guidance:

  • For refinery control problems with high uncertainty and multiple expert perspectives, implement D-SFS with CoCoSo integration
  • For scenarios requiring rapid preliminary analysis with limited computational resources, standard CoCoSo provides efficient solutions
  • For decisions involving conflicting technical, economic and environmental criteria, leverage the D-SFS enhanced weighting approach

• Data Requirements and Preparation:

  • Ensure adequate expert representation across relevant refinery operational domains
  • Pre-process historical operational data to establish baseline performance metrics
  • Clearly define linguistic variables and their corresponding D-SFS representations before assessment

• Validation Protocol:

  • Implement cross-validation with historical refinery control decisions where possible
  • Conduct sensitivity analysis across expected parameter variation ranges
  • Compare results against established operational benchmarks specific to refining processes

The integration of D-SFS frameworks with CoCoSo methodology represents a significant advancement for handling complex decision scenarios in oil-refining unit control. This hybrid approach enables more faithful representation of uncertain operational parameters while providing robust ranking mechanisms for evaluating control strategies across multiple competing criteria.

The optimization of oil-refining units is a complex challenge that requires balancing multiple, often conflicting, objectives such as maximizing separation efficiency, minimizing energy consumption, and reducing operational costs. In this context, fuzzy multi-criteria decision-making (MCDM) emerges as a powerful tool to handle the inherent uncertainties and subjective judgments present in refinery operational data [1]. This document provides detailed application notes and experimental protocols for quantifying performance gains in oil-refining unit control, framed within a broader research thesis on fuzzy MCDM. It is designed to equip researchers and scientists with structured methodologies to collect, analyze, and interpret key performance data, thereby supporting more informed and robust decision-making for sustainable refining operations.

The following tables consolidate key quantitative performance indicators from various studies on refining processes, focusing on separation efficiency, energy consumption, and cost-related metrics. These data provide benchmarks for evaluating the effectiveness of optimization and control strategies.

Table 1: Performance Metrics for Demulsifier Selection in Crude Oil Dehydration

Demulsifier Alternative	Separation Efficiency	Environmental Impact	Cost-Effectiveness	Overall Closeness Coefficient
Nalco Champion EC7135A	High	Lower	Moderate	0.751
Alcopol 500	High	Moderate	High	0.708
Polymer-based Demulsifier	Moderate	Moderate	High	0.692
Schlumberger’s ClearPhase	Moderate	Higher	Moderate	0.619

Source: Adapted from [3]

Table 2: Energy and Emission Reduction Potentials in China's Petroleum Refining Industry

Performance Indicator	Baseline (2015)	Reduction Potential by 2050	Primary Contributing Process
Total Energy Use	-	12%	Heat Integration
CO₂ Emissions	9.76B tons (Nat'l)	10%	System-wide efficiency
SO₂ Emissions	-	2%	Catalytic Cracking
PM₂.₅ Emissions	-	1%	Catalytic Cracking
Circulating Water Consumption	-	7%	Process Optimization
Softened Water Consumption	-	80%	Advanced Treatment Technologies

Source: Adapted from [69]

Table 3: Advanced Technology Impacts on Crude Distillation Unit (CDU) Performance

Technology Intervention	Performance Gain	Key Impact Area
Advanced Column Designs (Dividing-wall, Hybrid Systems)	15-30% energy use reduction	Energy Consumption
Solar-Assisted Preheating	Up to 20% reduction in fossil fuel demand	Energy Consumption & Cost
AI-Based Optimization	Improved process stability and operational flexibility	Separation Efficiency & Cost
Green Hydrogen Integration	Strong decarbonization potential	Environmental Impact & Long-term Cost

Source: Adapted from [41]

Experimental Protocols and Methodologies

Protocol: Application of Fuzzy TOPSIS for Demulsifier Evaluation

Objective: To systematically rank demulsifier alternatives for crude oil dehydration using the Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS) [3].

Materials:

• Candidate demulsifiers (e.g., Alcopol 500, Polymer-based Demulsifier, Nalco Champion EC7135A, Schlumberger’s ClearPhase)
• Crude oil samples with known emulsion characteristics
• Standard bottle test apparatus (graduated cylinders, water bath, pipettes)
• Fuzzy evaluation software (e.g., MATLAB, Python with SciPy and NumPy libraries)

Procedure:

• Define Criteria and Alternatives: Identify key evaluation criteria: Separation Efficiency, Environmental Impact, Cost-Effectiveness, and Ease of Application. List all demulsifier alternatives to be evaluated.
• Construct Fuzzy Decision Matrix: Form a panel of at least three experts. For each alternative and criterion, have experts provide linguistic ratings (e.g., "Very High," "High," "Medium," "Low"). Convert these linguistic terms into corresponding fuzzy numbers (e.g., triangular or trapezoidal fuzzy numbers).
• Assign Criteria Weights: Experts assign linguistic importance weights to each criterion, which are also converted into fuzzy numbers.
• Build Weighted Fuzzy Decision Matrix: Normalize the fuzzy decision matrix and multiply it by the fuzzy weights to construct the weighted normalized fuzzy decision matrix.
• Determine Fuzzy Ideal Solutions: Identify the Fuzzy Positive Ideal Solution (FPIS) and Fuzzy Negative Ideal Solution (FNIS). The FPIS is the maximum positive value for each criterion, while the FNIS is the least desirable value.
• Calculate Separation Measures: For each alternative, compute the distance from the FPIS and the FNIS using an appropriate distance measure for fuzzy numbers (e.g., vertex method).
• Calculate Closeness Coefficient and Rank: The closeness coefficient (CCᵢ) for each alternative i is calculated as CCᵢ = dᵢ⁻ / (dᵢ⁺ + dᵢ⁻), where dᵢ⁻ is the distance from FNIS and dᵢ⁺ is the distance from FPIS. Rank alternatives in descending order of CCᵢ; the alternative with the highest CCᵢ is the most preferable.

Protocol: Heuristic Fuzzy Multi-Criteria Decision Making for Stabilization Column Control

Objective: To optimize the operating parameters of a stabilization column in a primary oil-refining unit using a heuristic fuzzy MCDM method that combines the main criterion and maximin principles [1].

Materials:

• Operational data from the target stabilization column
• Sensors and data acquisition system for temperature, pressure, and flow rates
• Fuzzy modeling and optimization software platform

Procedure:

• System Identification and Fuzzy Modeling: Develop a fuzzy model of the stabilization column using experimental-statistical methods and expert evaluations. The model should relate input operating parameters (e.g., feed temperature, reflux ratio) to output performance criteria (e.g., product quality, energy consumption).
• Formulate the Fuzzy Decision-Making Problem: Define the set of alternatives (different combinations of operating parameters) and the multiple, conflicting criteria for evaluation. Criteria often include technical performance (separation quality) and economic factors (operating cost).
• Apply the Heuristic Method: Utilize the developed heuristic method based on the main criterion and maximin principle [1].
  • Main Criterion Principle: Select the most important criterion. Find alternatives that provide the best values for this main criterion while ensuring other criteria meet acceptable threshold levels defined by the decision-maker.
  • Maximin Principle: For each alternative, identify the criterion on which it has the worst (minimum) performance relative to its goal. Select the alternative for which this worst performance is the best (maximized) among all alternatives. This principle prioritizes robustness.
• Iterative Improvement: The method allows for iterative refinement of the solution by incorporating additional preferences from the decision-maker, leading to an effective and adequate final decision without converting the fuzzy problem into a set of crisp problems.

Protocol: Energy Efficiency and Emission Assessment using the MESSAGEix-Petroleum Refining Model

Objective: To quantify energy saving and emission mitigation potentials at the process level within a petroleum refining system [69].

Materials:

• Refinery process flow data (capacity, feedstock, product slate)
• Unit-level energy consumption and emission factor data
• MESSAGEix modeling framework with the developed petroleum refining extension

Procedure:

• System Characterization: Map the complex refining system by characterizing the technical features and interrelationships of all refining units (e.g., crude distillation, catalytic cracking, hydrotreating).
• Model Development: Develop the MESSAGEix-petroleum refining model by inputting the process flow data, energy consumption patterns, and emission factors for each unit operation.
• Scenario Definition: Define a baseline scenario reflecting current operations and an energy efficiency scenario incorporating best available technologies and practices (e.g., enhanced heat integration, waste heat recovery).
• Simulation and Analysis: Run the model to simulate energy consumption and emissions (CO₂, NOₓ, SO₂, PM₂.₅) under both scenarios at the overall sector and individual process levels.
• Potential Quantification: Calculate the difference in energy use and emissions between the baseline and efficiency scenarios to determine the maximum reduction potential for each metric. Analyze which processes contribute most significantly to the reduction potential.

Workflow and Signaling Pathways

The following diagram illustrates the logical workflow for applying fuzzy MCDM to the control and optimization of an oil-refining unit, integrating the protocols described above.

Diagram 1: Fuzzy MCDM Workflow for Refining Unit Optimization.

The Scientist's Toolkit: Research Reagent Solutions

Table 4: Essential Materials and Tools for Fuzzy MCDM in Oil-Refining Research

Item Name	Function/Application	Specification Notes
Commercial Demulsifiers (e.g., Nalco Champion EC7135A, Alcopol 500)	Used in dehydration experiments to break water-in-crude-oil emulsions, directly impacting separation efficiency metrics.	Selection should be based on the specific crude oil blend; performance varies with chemical composition [3].
Fuzzy Logic Modeling Software (e.g., MATLAB Fuzzy Logic Toolbox, Python with scikit-fuzzy)	Core platform for developing fuzzy inference systems, fuzzifying data, and implementing MCDM algorithms like FTOPSIS.	Essential for handling the uncertainty and subjectivity in expert judgments and process data [1] [8].
Process Simulation Software (e.g., Aspen HYSYS, MESSAGEix-Petroleum Refining Model)	Models energy flows, mass balances, and emission generation at the unit-operation level to provide quantitative data for criteria weighting.	The MESSAGEix framework is specifically adapted for refinery-wide energy and emission analysis [69].
Picture Fuzzy Inference System (PFIS)	A specialized fuzzy tool for criticality analysis of refinery assets, handling membership, non-membership, and hesitancy degrees for more nuanced uncertainty management.	Particularly advantageous when expert assessments include significant hesitation or lack of quantitative data [8].
Data Acquisition System (Sensors for T, P, flow rate)	Collects real-time operational data from refining units (e.g., stabilization column, CDU) for model validation and performance monitoring.	Data quality is critical for developing accurate fuzzy models and for the subsequent validation of decision outcomes [1].

Validation Through Industrial Case Studies on Crude Oil Dehydration and Desalting

Crude oil dehydration and desalting are critical pretreatment processes in petroleum refining, directly impacting product quality, operational efficiency, and facility corrosion prevention. The formation of stable water-in-crude oil emulsions, stabilized by natural surfactants like asphaltenes, resins, and waxes, presents a persistent technical challenge [3]. Effective breaking of these emulsions is essential for removing water and salts, particularly in mature fields with higher water cuts and fine solids content that increase emulsion stability and treatment complexity [70].

This document presents application notes and experimental protocols framed within a broader thesis on fuzzy multi-criteria decision-making (FMCDM) for oil-refining unit control. The integration of FMCDM methodologies addresses the complex, multi-variable optimization challenges inherent in dehydration and desalting processes, where operational parameters interact in non-linear ways under uncertain conditions [1] [3]. We provide validated industrial case data, detailed experimental protocols, and decision-support frameworks to enhance research and development in petroleum processing optimization.

Industrial Context and Economic Significance

The global oil refining market, valued at approximately $1.84 trillion in 2024, is projected to reach $2.80 trillion by 2034, growing at a CAGR of 4.30% [71]. This growth occurs despite increasing pressure on refiners from alternative energy sources and environmental regulations. Refining margins have tightened significantly, with downstream earnings for integrated oil companies dropping by approximately 50% in 2024 over 2023 and about 60% lower than 2022 levels [16]. In this competitive landscape, optimizing fundamental processes like dehydration and desalting becomes crucial for maintaining profitability.

Table 1: Global Oil Refining Market Outlook

Parameter	2024 Value	2034 Projected	CAGR (2025-2034)
Market Size	$1,838.46 billion	$2,800.91 billion	4.30%
Asia Pacific Market Size	$680.23 billion	$1,050.34 billion	4.44%
Refining Capacity Change (2025)	-188,000 b/d	-	-
Singapore Gross Refinery Margin	~$6.8/bbl	$5.5-6.0/bbl (2025-2027)	-

Complex refineries with high Nelson Complexity Index (NCI) values possess greater flexibility in processing various crude types and converting heavy fractions to higher-value products [39]. Efficient dehydration and desalting are particularly crucial for these facilities as they enable processing of opportunity crudes with higher emulsion tendencies, potentially improving gross refinery margins by $0.40 to $1.45 per barrel through advanced optimization techniques [16].

Technical Background: Dehydration and Desalting Fundamentals

Crude oil emulsions form during production due to shear forces and the presence of natural emulsifiers. Dehydration removes emulsified water, while desalting removes dissolved salts (primarily chlorides) through water washing. Electrostatic treaters applying AC, DC, or combined AC-DC fields are commonly used to promote water droplet coalescence [70]. Mature fields present particular challenges with higher water cuts creating more stable emulsions with increased viscosity, often requiring higher operating temperatures and chemical demulsifier doses [70].

The performance of dehydration and desalting processes is typically measured through:

• Water Removal Efficiency (WRE): Percentage of water removed from the crude oil emulsion
• Salt Removal Efficiency (SRE): Percentage of salts removed from the crude oil
• Interface Quality: Sharpness of oil-water separation
• Effluent Water Quality: Oil content in discharged water

Application of Fuzzy Multi-Criteria Decision Making

Traditional approaches to dehydration/desalting optimization often rely on single-criterion assessments or trial-and-error methods. Fuzzy MCDM methodologies address the inherent uncertainty and multiple, often conflicting, criteria in process optimization [1]. In petroleum operations, where system characterization involves "fuzzy initial information" [1], these approaches enable more adequate decision-making by maximizing the use of available fuzzy information.

The Fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) has demonstrated particular utility in demulsifier selection, handling uncertainty and vagueness in criteria evaluations through fuzzy logic [3]. This approach evaluates alternatives based on their relative closeness to an ideal solution while considering multiple criteria simultaneously, including separation efficiency, cost, environmental impact, and operational feasibility [3].

Case Study: Optimization of Dehydration/Desalting Efficiency

Experimental Design and Response Surface Methodology

A comprehensive optimization study investigated water separation from crude oil emulsions under static and dynamic conditions using Central Composite Design of Response Surface Methodology (CCD-RSM) [72]. The research evaluated four key operational parameters across multiple levels to determine their individual and interactive effects on dehydration and desalting performance.

Table 2: Operational Parameters and Levels for CCD-RSM Experimental Design

Parameter	Low Level	High Level	Optimal Value
Demulsifier Concentration	5 ppm	25 ppm	19.5 ppm
Temperature	90°C	130°C	125°C
Oil Space Velocity	0.5 1/h	1.5 1/h	1 1/h
Wash Water Ratio	2 vol%	8 vol%	6 vol%

The experimental design enabled developing RSM-based models to forecast demulsification efficiency (WRE and SRE) and conduct sensitivity analysis to determine parameter influences [72]. The separation effectiveness was analyzed by evaluating both Water-Removal-Efficiency (WRE) and Salt-Removal-Efficiency (SRE).

Results and Optimal Conditions

The study demonstrated that demulsifier type and concentration had the greatest impact on dehydration efficiency (F-value = 434.56) [72]. Sensitivity analysis indicated that the dehydration/desalting process is also highly sensitive to oil space velocity and wash water ratio, while showing less sensitivity to temperature variations [72].

Table 3: Dehydration/Desalting Performance at Optimal Conditions

Performance Metric	Value at Optimal Conditions
Water Removal Efficiency (WRE)	94.54%
Salt Removal Efficiency (SRE)	97.23%
Demulsifier Concentration	19.5 ppm
Temperature	125°C
Oil Space Velocity	1 1/h
Wash Water Ratio	6 vol%

The achieved performance at these optimal conditions demonstrates the effectiveness of systematic parameter optimization, with simultaneous high efficiency in both water and salt removal [72].

Experimental Protocols

Bottle Test Protocol for Demulsifier Screening

Purpose: To evaluate demulsifier performance under static conditions through standardized bottle tests.

Materials:

• Crude oil emulsion sample
• Selected demulsifiers
• Graduated conical tubes (100 mL)
• Water bath with temperature control
• Timer
• Pipettes

Procedure:

• Sample Preparation: Homogenize the crude oil emulsion to ensure uniform water distribution.
• Dosing: Add varying concentrations of demulsifier (5-25 ppm) to separate 100 mL emulsion samples in graduated conical tubes.
• Mixing: Agitate each tube consistently (e.g., 100 inversions) to ensure complete demulsifier distribution.
• Incubation: Place tubes in water bath maintained at test temperature (e.g., 125°C).
• Monitoring: Record separated water volume at regular intervals (5, 10, 15, 30, 60, 120 minutes).
• Evaluation: Calculate WRE based on total water separated versus initial water content.

Evaluation Criteria: Separation efficiency, separation rate, interface quality, water clarity.

Electrostatic Dehydration Pilot Plant Protocol

Purpose: To investigate dehydration performance under dynamic conditions simulating industrial operations.

Equipment: Electrostatic desalting pilot plant with adjustable parameters.

Procedure:

• System Calibration: Verify electrostatic field generation, temperature control, and flow metering.
• Parameter Setting: Configure operational parameters according to experimental design (temperature, oil space velocity, wash water ratio, demulsifier concentration).
• System Stabilization: Run system until stable operation is achieved at set parameters.
• Sample Collection: Collect treated crude oil samples at system outlet after residence time stabilization.
• Analysis: Determine residual water and salt content in treated crude per ASTM methods.
• Data Recording: Document all operational parameters and corresponding performance metrics.

Evaluation Metrics: WRE, SRE, power consumption, effluent water quality.

Fuzzy TOPSIS Protocol for Demulsifier Selection

Purpose: To systematically rank demulsifier alternatives using fuzzy multi-criteria decision making [3].

Procedure:

• Criteria Definition: Establish evaluation criteria (separation efficiency, environmental impact, cost, ease of application).
• Weight Assignment: Assign fuzzy weights to each criterion based on expert judgment.
• Alternative Evaluation: Assess each demulsifier against all criteria using linguistic variables converted to fuzzy numbers.
• Fuzzy Decision Matrix: Construct fuzzy decision matrix incorporating all assessments.
• Normalization: Normalize the fuzzy decision matrix to enable cross-criterion comparison.
• Weighted Matrix: Calculate weighted normalized fuzzy decision matrix.
• Ideal Solutions: Determine fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS).
• Distance Calculation: Calculate distances of each alternative from FPIS and FNIS.
• Closeness Coefficient: Compute closeness coefficient for each alternative.
• Ranking: Rank alternatives based on descending closeness coefficient values.

The Scientist's Toolkit: Research Reagent Solutions

Table 4: Essential Materials for Crude Oil Dehydration Research

Material/Reagent	Function	Application Notes
Non-ionic Demulsifiers	Breaks water-in-oil emulsions by disrupting interfacial films	Alcopol 500, Polymer-based Demulsifier, Nalco Champion EC7135A, Schlumberger's ClearPhase show varying efficacy [3]
AC-DC Electrostatic Treater	Promotes water droplet coalescence via electrostatic fields	Particularly effective for mature fields with high water cuts; retrofitting existing AC treaters improves performance [70]
Composite Electrode Plates	Enhances electrostatic field distribution	Improves dehydration efficiency in treaters; enables operation with higher water-cut crudes [70]
Wash Water	Dilutes and removes salts from crude oil	Optimal ratio typically 4-8 vol%; affects both desalting efficiency and operating costs [72]
Crude Oil Samples	Test substrate for dehydration studies	Varying composition (asphaltenes, resins, wax content) significantly impacts emulsion stability [3]

Integration with Fuzzy Multi-Criteria Decision Making

The application of fuzzy MCDM, particularly fuzzy TOPSIS, has demonstrated significant advantages in demulsifier selection. In comparative studies, Nalco Champion EC7135A achieved the highest closeness coefficient (0.751), followed by Alcopol 500 (0.708), Polymer-based Demulsifier (0.692), and Schlumberger's ClearPhase (0.619) [3]. This structured approach quantifies expert evaluations and manages the inherent uncertainty in performance predictions.

The fuzzy MCDM framework enables researchers to:

• Systematically manage vague or incomplete information common in crude oil characterization
• Balance multiple, often competing objectives (efficiency, cost, environmental impact)
• Incorporate expert knowledge through fuzzy linguistic variables
• Provide transparent and reproducible decision-making processes
• Adapt to varying operational priorities and constraints

For oil refining unit control, these methods allow iterative improvement of operating modes by maximizing the use of collected fuzzy information, leading to more adequate decisions in environments characterized by uncertainty [1].

This application note has presented comprehensive industrial case studies and experimental protocols for validating crude oil dehydration and desalting processes. The integration of fuzzy multi-criteria decision-making methodologies provides a robust framework for optimizing these critical pretreatment operations amid the complex, uncertain conditions characteristic of petroleum refining.

The documented optimal conditions (19.5 ppm demulsifier concentration, 125°C temperature, 1 1/h oil space velocity, and 6 vol% wash water ratio) achieving 94.54% WRE and 97.23% SRE demonstrate the significant efficiency improvements possible through systematic optimization [72]. Furthermore, the application of fuzzy TOPSIS for demulsifier selection enhances decision quality by comprehensively evaluating multiple criteria under uncertainty [3].

These protocols and case studies provide researchers with validated methodologies for advancing dehydration and desalting operations while contributing to the broader thesis on fuzzy multi-criteria decision-making for oil-refining unit control. The integration of systematic experimental design with computational decision-support frameworks represents a powerful approach for addressing the complex optimization challenges in petroleum processing.

Assessing the Transparency, Reliability, and Adaptability of Different FMCDM Frameworks

Fuzzy Multi-Criteria Decision-Making (FMCDM) has emerged as a vital methodology for addressing complex industrial problems characterized by imprecise information, multiple conflicting criteria, and subjective human judgment. Within the specific context of oil-refining unit control, where processes like stabilizing column operation are influenced by numerous non-formalizable parameters, FMCDM provides a structured framework for optimizing operating modes amid uncertainty [1]. The performance of these frameworks hinges critically on three interconnected pillars: transparency (the clarity and auditability of the decision process), reliability (the stability and robustness of results), and adaptability (the capacity to handle diverse, evolving, and fuzzy data) [73] [74].

This document provides detailed application notes and experimental protocols for the quantitative assessment of these characteristics in FMCDM frameworks. The protocols are contextualized for researchers and scientists developing control systems for primary oil-refining units, guiding the evaluation and selection of appropriate FMCDM methods for specific operational challenges.

Framework Assessment and Comparative Analysis

A critical first step is the systematic comparison of prevalent FMCDM methods. The following table synthesizes their key attributes concerning transparency, reliability, and adaptability.

Table 1: Comparative Analysis of Fuzzy Multi-Criteria Decision-Making (FMCDM) Frameworks

FMCDM Method	Transparency & Explainability	Reliability & Robustness	Adaptability to Fuzzy Data & Problem Types	Common Hybridizations
Fuzzy AHP (FAHP)	High, due to structured hierarchy and pairwise comparisons; but can suffer from expert bias [75] [76].	Moderate; susceptible to ranking inconsistencies with criteria interdependence [77]. Requires consistency index validation [76].	High for weighting criteria in fuzzy environments; effective for integrating expert linguistic judgments [76] [73].	Often integrated with FTOPSIS, FVIKOR, and fuzzy comprehensive evaluation (FCE) [75] [76].
Fuzzy TOPSIS (FTOPSIS)	Intuitive logic based on distance from ideal solution; process is easily traceable, enhancing transparency [78] [77].	High, especially when combined with sensitivity analysis on weights and fuzzy numbers [78] [79]. Min-max operations can reduce comparison complexity [78].	Highly adaptable to various fuzzy set types (e.g., interval-valued, spherical) [78] [73]. Well-suited for screening a large number of alternatives.	Commonly paired with FAHP for weighting and FTOPSIS for ranking [76] [77].
Fuzzy VIKOR	High; provides a compromise solution with an explicit "regret" measure, making the trade-off logic clear to decision-makers [80].	High; designed to find stable compromises, often validated via sensitivity analysis to weight variations [80] [79].	Effective for problems with conflicting and non-commensurable criteria where a negotiable solution is acceptable [80].	Used with DEMATEL and ANP in hybrid models for complex interdependencies [79].
Fuzzy ELECTRE	Moderate; outranking relations can be complex to explain to non-experts, reducing transparency [79].	High in handling non-compensatory criteria; robust for problems where veto thresholds are present [79].	Adaptable to fuzzy environments where incomparability between alternatives is possible and acceptable [79].	Less commonly hybridized than AHP/TOPSIS but used in specific complex scenarios [79].
Hybrid Methods (e.g., MARCOS with Objective Weights)	Very High; reduces subjectivity using objective weighting (Entropy, CRITIC), enhancing reproducibility and transparency [80].	Very High; achieves high stability indices (e.g., >0.9) across perturbation scenarios, confirming robustness [80].	High; Bonferroni operator fusion of weighting methods adapts to different data structures within the same problem [80].	Integrates multiple objective weighting methods (Entropy, CRITIC, MEREC) with a ranking method (MARCOS) [80].

Detailed Experimental Protocols for FMCDM Evaluation

Protocol 1: Quantitative Assessment of Framework Transparency

Objective: To measure the explainability and auditability of an FMCDM process using a standardized scoring system. Application Context: Evaluating control strategies for a primary oil-refining stabilization column [1].

Methodology:

• Define Transparency Metrics: Establish a scorecard (0-10 points per metric) for the FMCDM process.
  • Data Provenance (10 pts): Full traceability of all input data, including expert judgments and sensor readings.
  • Weight Justification (10 pts): Clear documentation of criteria weight derivation (e.g., objective vs. subjective methods).
  • Algorithmic Clarity (10 pts): The ranking or selection logic is accessible to a non-expert audience.
  • Result Interpretability (10 pts): The final output provides clear reasoning for the ranking.

• Execute FMCDM Process: Apply the FMCDM framework to a case study, such as optimizing the temperature and pressure parameters of a stabilization column.

• Calculate Transparency Index: Sum the scores from the four metrics. A higher total score indicates greater framework transparency. This index allows for the direct comparison of different FMCDM methods.

Protocol 2: Sensitivity Analysis for Framework Reliability

Objective: To test the robustness and stability of an FMCDM framework's rankings against variations in input data and parameters. Application Context: Ensuring the selected operating mode for a catalytic reforming unit remains optimal under data uncertainty [1] [4].

Methodology:

• Establish Baseline Ranking: Run the FMCDM model with the original dataset and weights to establish a baseline ranking of control alternatives.

• Introduce Systematic Perturbations:

  • Criteria Weight Perturbation: Systematically vary each criterion's weight by ±5%, ±10%, and ±15%, one at a time, while adjusting the others proportionally.
  • Fuzzy Number Perturbation: Alter the boundaries of the triangular or trapezoidal fuzzy numbers representing uncertain parameters (e.g., "high temperature") by a small percentage (e.g., ±5%).

• Stability Calculation: After each perturbation, re-run the model and record the new ranking.

  • Calculate Spearman’s Rank Correlation Coefficient (ρ) between the baseline ranking and each perturbed ranking.
  • A framework is considered highly reliable if the average ρ across all perturbations is ≥ 0.9 [80].

Protocol 3: Evaluating Adaptability to Fuzzy Data

Objective: To assess the framework's capability to process different types of fuzzy input and produce stable outputs. Application Context: Incorporating expert knowledge and imprecise sensor data into the control model for a stabilization column [1].

Methodology:

• Select Fuzzy Set Types: Test the FMCDM framework using at least three different types of fuzzy sets:
  • Triangular Fuzzy Numbers (TFNs)
  • Interval-Valued Fuzzy Sets (IVFSs)
  • Pythagorean Fuzzy Sets (PFSs) [73]

• Input Variation: Use each fuzzy set type to represent the same set of linguistic variables (e.g., "high pressure," "low efficiency") from experts.

• Output Consistency Analysis: Execute the FMCDM process for each fuzzy set type.

  • Compare the final rankings using Kendall’s W Coefficient of Concordance.
  • A high W value (e.g., > 0.8) indicates that the framework's output is consistent regardless of the fuzzy set type used, demonstrating high adaptability.

Workflow Visualization for FMCDM Assessment

The following diagram outlines the core experimental workflow for a comprehensive assessment of an FMCDM framework, integrating the protocols defined above.

Diagram 1: FMCDM Assessment Workflow

The Scientist's Toolkit: Key Research Reagents and Materials

Table 2: Essential Research Reagents and Computational Tools for FMCDM in Oil-Refining Research

Item / Tool	Function / Description	Application Note
Expert Panel	Provides qualitative, linguistic judgments (e.g., "very important," "high risk") which are converted into fuzzy numbers.	Crucial for defining criteria weights and performance ratings in the absence of precise quantitative data [1] [76].
Fuzzy Set Types (TFNs, IVFSs, PFSs)	Mathematical structures for representing and computing with vague or imprecise information.	The choice of fuzzy set (Triangular, Interval-Valued, Pythagorean) impacts the model's ability to capture different types of uncertainty [73].
Objective Weighting Methods (Entropy, CRITIC)	Algorithms to determine criteria weights based solely on the data structure, minimizing subjectivity.	Enhances transparency and reproducibility. CRITIC accounts for correlation between criteria, while Entropy measures the amount of information [80].
Sensitivity Analysis Scripts	Custom code (e.g., in Python or R) to automate weight and parameter perturbations.	Essential for quantitatively evaluating the reliability of the FMCDM framework as per Protocol 2 [80] [79].
MCDM Software Libraries (e.g., PyDecision, MCDA)	Pre-built code libraries that implement common MCDM algorithms.	Accelerates prototyping and application of methods like TOPSIS, VIKOR, and AHP, but requires validation for fuzzy extensions [77].

Conclusion

The application of Fuzzy Multi-Criteria Decision-Making presents a transformative, data-driven approach for optimizing control in oil-refining units, effectively handling the inherent uncertainty and conflicting objectives of industrial operations. Methodologies like Fuzzy TOPSIS and advanced frameworks based on Disc Spherical Fuzzy Sets have demonstrated superior performance in practical applications, from demulsifier selection to the optimization of stabilization columns, leading to measurable improvements in separation efficiency, cost-effectiveness, and environmental compliance. Future advancements in this field are poised to integrate real-time operational data with predictive machine learning models, further enhancing decision accuracy. The exploration of emerging, eco-friendly processes and the continuous development of sophisticated fuzzy aggregation operators will be crucial for meeting the evolving challenges of sustainable and efficient petroleum refining.

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