A Distance Measure of Fermatean Fuzzy Sets Based on Triangular Divergence and its Application in Medical Diagnosis

Abstract

Fermatean fuzzy sets (FFSs), as one of the representative variants of fuzzy sets, have broad application prospects. FFSs have advantages in modeling uncertain information and therefore have been widely applied. However, how to perfectly quantify the differences between FFS remains an open question. This paper introduces a new distance measure for FFSs, utilizing triangular divergence. The proposed measure is designed to rectify the limitations in the current measure, offering a more effective solution for analyzing FFSs. Moreover, we demonstrate that the proposed distance measure satisfies some basic properties and further show its effectiveness through several numerical examples. Finally, we explore the performance of the proposed distance measure in a medical diagnosis application, and the results show that the proposed distance measure can well overcome the limitations of the current measure.