Fermatean Fuzzy Graph in Decision-Making Models Theory

Resumen

Fermatean Fuzzy Graph (FFG) is a prominent mathematical model effective in conveying uncertainty, hesitation and dual membership characteristics in decision-making domains where traditional models often exhibit ineptness in handling complex ambiguities. Thereby, an extensive investigation of Fermatean fuzzy graphs within decision-making frameworks is executed in this study to emphasise their theoretical underpinnings, structural attributes and practical implications. Through the extension of Fermatean fuzzy set theory, the proposed model represents each vertex and edge with cubic membership, non-membership and hesitation degrees. This in turn results in the enrichment of the descriptive capacity of relational data structures. Key operations including union, intersection, complement and Cartesian product are formulated in the study under Fermatean conditions, and their algebraic and topological features are then thoroughly discussed. In order to support multi-criteria evaluations in contexts characterised by ambiguity and contradicting information, the developed decision-making model incorporates FFG structures with weighted aggregation operators and similarity measures. The superior ability of FFGs to handle uncertainty with enhanced precision and decision dependability is demonstrated by comparison with intuitionistic and Pythagorean fuzzy graph models.