Advancing decision making with distance and similarity measures for belief and plausibility in Fermatean fuzzy sets.

Fermatean fuzzy sets (FFSs) have become a potent tool for modeling uncertainty in decision-making, offering a higher degree of flexibility compared to traditional fuzzy and intuitionistic fuzzy sets (IFSs). Within the context of evidence theory, the notions of belief and plausibility enhance the representational capacity of FFSs, enabling the handling of ambiguous and conflicting data. This study proposes advanced constructions of distance and similarity measures for belief and plausible Fermatean fuzzy sets (BP-FFSs). These measures are designed to capture nuanced differences and relationships among BP-FFSs, addressing critical gaps in existing methodologies. The proposed measures are rigorously evaluated for essential mathematical properties. Furthermore, their effectiveness is validated through real-world applications in fields such as pattern identifications, multi-criteria decision-making (MCDM) and medical diagnosis. Numerical analyses using variety of problems demonstrate the superiority and robustness of the suggested approach in handling complex uncertainty scenarios. This research contributes to the theoretical foundation of fuzzy set theory (FST) and its practical applications, offering a comprehensive framework that advances both the understanding and utilization of BP-FFSs. The findings underscore the potential of the proposed measures in addressing contemporary challenges across diverse domains.