Fermatean Fuzzy Multi-Criteria Decision-Making Methoden
Summary
Fermatean fuzzy multi-criteria decision-making (MCDM) methods employ an advanced fuzzy-set framework in which the squared sum of membership, non-membership and hesitancy degrees does not exceed unity. This richer expressive power over conventional and intuitionistic fuzzy systems permits more nuanced modelling of expert judgement under uncertainty. By integrating Fermatean fuzzy sets with established MCDM techniques—such as DEMATEL, PROMETHEE, TOPSIS and Heronian mean operators—researchers can derive criteria weights, aggregate preferences and rank alternatives in contexts ranging from industrial development to sustainable urban transport. The approach enhances robustness in the presence of incomplete or ambiguous information and supports strategic planning in complex socio-technical systems. Globally, these methods have found application in supply-chain resilience, digital transformation, infrastructure planning and environmental decision-making, demonstrating both theoretical maturity and practical relevance.
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Technical terms
Fermatean fuzzy set: A fuzzy-set model with membership, non-membership and hesitancy values whose squared sum does not exceed one, allowing greater uncertainty representation.
Multi-Criteria Decision-Making (MCDM): A collection of methods for ranking and selecting alternatives based on multiple, often conflicting criteria under uncertainty.
DEMATEL: Decision-Making Trial and Evaluation Laboratory, a network-analysis tool to determine and visualise causal relationships among decision criteria.
PROMETHEE-II: Preference Ranking Organisation METHod for Enrichment Evaluations, a pairwise comparison algorithm that produces a complete ranking of alternatives.
CRITIC method: Criteria Importance Through Intercriteria Correlation, an objective weighting technique that accounts for both contrast intensity and criterion interdependence.
References
- Evaluating the Interrelationships of Industrial 5.0 Development Factors Using an Integration Approach of Fermatean Fuzzy Logic. Journal of Operations Intelligence (2024).
- Analyzing the barriers to resilience supply chain adoption in the food industry using hybrid interval-valued fermatean fuzzy PROMETHEE-II model. Journal of Industrial Information Integration (2024).
- Unveiling the implementation barriers to the digital transformation in the energy sector using the Fermatean cubic fuzzy method. Applied Energy (2024).
- Fermatean fuzzy Archimedean Heronian Mean-Based Model for estimating sustainable urban transport solutions. Engineering Applications of Artificial Intelligence (2024).
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