Fuzzy Logic-Based Multi-Criteria Decision-Making Methods (Fuzzy MCDM)

Traditional decision-making approaches provide solutions based on precise and clear data; however, decision-makers often encounter situations involving uncertainty and vagueness in real life. In such cases, traditional Multi-Criteria Decision-Making Techniques (MCDM) may have some limiting factors. At this point, fuzzy logic comes into play, enabling decision-makers to handle uncertainty more effectively. Fuzzy logic-based MCDM approaches offer the capability to process ambiguous data sets without strict boundaries. This article examines fuzzy logic-based multi-criteria decision-making techniques and provides details about these methods.

Fuzzy logic, developed by Zadeh in 1965, is an approach based on "degrees of truth" rather than the binary true/false system of classical logic. While traditional logic dictates that a statement is either true or false, fuzzy logic represents the degree of truth on a scale from 0 to 1, providing a more flexible decision-making mechanism. Thus, real-world scenarios involving uncertainty can be analyzed more effectively.

• Description: Fuzzy AHP adapts traditional AHP to decision problems involving uncertainty by expressing subjective judgments of decision-makers using fuzzy triangular numbers. Its hierarchical structure simplifies the analysis of complex decision problems by breaking them into sub-problems.
• First Application Example: Proposed by Chang (1996), fuzzy AHP introduced an extent analysis method to determine criteria weights using fuzzy logic.
• Applications: Strategic planning, resource allocation, project management, infrastructure project evaluations.
• Advantages: Handles uncertainty effectively, incorporates subjective judgments, and systematizes the decision-making process.
• Disadvantages: More complex than traditional AHP and prone to errors during the creation of comparison matrices.

• Description: Fuzzy TOPSIS ranks alternatives based on their closeness to the ideal solution. In uncertain conditions, criteria values and weights are expressed using fuzzy numbers. It provides a ranking based on the distance from the ideal (best) and negative ideal (worst) solutions.
• First Application Example: Developed by Chen (2000), fuzzy TOPSIS was used to manage uncertainties in group decision-making problems.
• Applications: Performance evaluation, supplier selection, risk management, service quality analysis.
• Advantages: Relatively simple computational processes and effective solutions for uncertain and conflicting data. Supports decision-making with visual and numerical outcomes.
• Disadvantages: Defining uncertainty parameters accurately can be challenging. Precise determination of weights is critical.

• Description: Fuzzy PROMETHEE expresses criterion values and preference functions using fuzzy numbers to rank alternatives. The superiority of alternatives relative to one another is determined using preference functions, which thoroughly consider the priorities of decision-makers.
• First Application Example: Behzadian et al. (2010) integrated fuzzy logic into PROMETHEE, offering applicability for ranking alternatives in uncertain decision-making environments.
• Applications: Project evaluation, investment decisions, environmental impact assessment.
• Advantages: Flexible and capable of handling uncertainty. Reflects user preferences directly.
• Disadvantages: Determining preference functions requires expertise. Computational processes may be time-consuming with large datasets.

• Description: Provides compromise solutions by balancing the distances of alternatives to the ideal solution. Fuzzy logic expresses criteria values under uncertainty. The main goal of VIKOR is to offer a compromise degree that helps decision-makers find the most suitable solution.
• First Application Example: Developed by Opricovic and Tzeng (2004), fuzzy VIKOR supported decision-making under uncertainty by offering compromise solutions.
• Applications: Strategic planning, investment decisions, product development.
• Advantages: Offers balanced decision-making and manages uncertainty effectively. Produces effective results, especially when conflicting criteria are present.
• Disadvantages: Requires precise definition of weights and parameters. Subjective decisions may lead to different outcomes.