Enhancing Similarity and Distance Measurements in Fermatean Fuzzy Sets: Tanimoto-Inspired Measures and Decision-Making Applications

Fermatean fuzzy sets (FFSs) serve as a nascent yet potent approach for coping with fuzziness, with their efficacy recently being demonstrated across a spectrum of practical contexts. Nevertheless, the scholarly literature remains limited in exploring the similarity and distance measures tailored for FFSs. The limited existing measures on FFSs sometimes yield counter-intuitive outcomes, which can obfuscate the accurate quantification of similarity and difference among FFSs. This paper introduces a suite of similarity and distance measures tailored for FFSs, drawing inspiration from the Tanimoto measure. We delve into the characteristics of these novel measures and offer some comparative studies with existing FFSs measures, highlighting their superior efficacy in the processing of fuzzy data from FFSs. Our proposed measures effectively rectify the counter-intuitive situations encountered with many existing measures and demonstrate a significant enhancement in differentiating between diverse FFSs. Moreover, we showcase the real-world applicability of our proposed measures through case studies in pattern recognition, medical diagnostics, and multi-attribute decision-making.