Multi-Criteria Decision Making Techniques with Fuzzy Logic (Fuzzy MCDM Techniques)

Traditional decision making approaches provide solutions based on precise and clear data, but in real-life situations, decision makers often encounter conditions characterized by uncertainty and ambiguity. In such cases, traditional Multi-Criteria Decision Making Techniques (MCDM) may have certain 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 ability to process data sets that lack sharp boundaries and are imprecise.

Fuzzy Logic

Fuzzy logic is an approach developed by Zadeh in 1965 that replaces classical logic, which relies on sharp boundaries, with the concept of "degrees of truth". In classical logic, a statement is either true or false. Fuzzy logic, however, expresses the degree of truth of a property on a scale between 0 and 1, providing a more flexible decision-making mechanism. This allows uncertain situations encountered in real life to be analyzed more effectively.

Fuzzy Logic with MCDM Methods

Fuzzy AHP (Analytic Hierarchy Process)

• Fuzzy AHP has been developed by adapting classical AHP to decision problems involving uncertainty. It is based on expressing the decision maker's subjective judgments regarding criteria and alternatives using fuzzy triangular numbers. Thanks to its hierarchical structure, complex decision problems are broken down into subproblems for easier analysis.
• Chang (1996) proposed a fuzzy AHP method that uses fuzzy logic to determine criterion weights through a extent analysis technique.
• It is applied in strategic planning, resource allocation, project management, and evaluation of infrastructure projects.
• Its advantages include: ability to handle uncertainty, incorporation of subjective judgments into the system, and systematization of the decision-making process.
• Its disadvantages include: a more complex computational process compared to classical AHP, and susceptibility to errors during the construction of the comparison matrix.

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

• Fuzzy TOPSIS ranks alternatives based on their proximity to the ideal solution. In situations of uncertainty, criterion values and weights are expressed as fuzzy numbers. It provides a ranking based on the distance from both the ideal solution (best values) and the negative ideal solution (worst values).
• Fuzzy TOPSIS, developed by Chen (2000), has been used to manage uncertainties in group decision-making problems.
• It is applied in performance evaluation, supplier selection, risk management, and service quality analysis.
• Its advantages include: relatively simple computational procedures, effective solutions for uncertain and conflicting data, and support for decision making through both visual and numerical results.
• Its disadvantages include: difficulty in accurately defining uncertainty parameters, and the importance of precisely determining weights.

Fuzzy PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluation)

• Fuzzy PROMETHEE ranks alternatives by expressing criterion values and preference functions as fuzzy numbers. The superiority of one alternative over another is determined through preference functions. This method takes into account the decision maker's preferences in detail.
• Behzadian et al. (2010) integrated PROMETHEE with fuzzy logic to provide applicability for ranking alternatives in uncertain decision-making environments.
• It is applied in project evaluation, investment decisions, and environmental impact assessment.
• Its advantages include: flexibility and capacity to handle uncertainty, and direct reflection of user preferences.
• Its disadvantages include: the determination of preference functions requires expertise, and computational processes can be time-consuming with large data sets.

Fuzzy VIKOR (Vise Kriterijumska Optimizacija I Kompromisno Resenje)

• VIKOR provides compromise solutions by balancing the distances of alternatives from the ideal solution. Fuzzy logic is used to represent criterion values under uncertainty. The primary goal of VIKOR is to offer a degree of compromise that enables decision makers to identify the most suitable solution.
• Fuzzy VIKOR, developed by Opricovic and Tzeng (2004), supports decision making under uncertainty by providing compromise solutions.
• It is applied in strategic planning, investment decisions, and product development.
• Its advantages include: enabling balanced decision making and handling uncertainty, and producing effective results especially when conflicting criteria are involved.
• Its disadvantages include: the need for precise definition of weights and parameters, and the potential inclusion of subjective decisions that may lead to different outcomes.