An Intuitionistic Fuzzy Version of Hellinger Distance Measure and Its Application to Decision-Making Process

Abstract

Intuitionistic fuzzy sets (IFSs), as a representative variant of fuzzy sets, has substantial advantages in managing and modeling uncertain information, so it has been widely studied and applied. Nevertheless, how to perfectly measure the similarities or differences between IFSs is still an open question. The distance metric offers an elegant and desirable solution to such a question. Hence, in this paper, we propose a new distance measure, named DIFS, inspired by the Hellinger distance in probability distribution space. First, we provide the formal definition of the new distance measure of IFSs, and analyze the outstanding properties and axioms satisfied by DIFS, which means it can measure the difference between IFSs well. Besides, on the basis of DIFS, we further present a normalized distance measure of IFSs, denoted DIFS˜. Moreover, numerical examples verify that DIFS˜ can obtain more reasonable and superior results. Finally, we further develop a new decision-making method on top of DIFS˜ and evaluate its performance in two applications.