Intuitionistic fuzzy divergences: critical analysis and an application in figure skating

Abstract

Despite the importance of divergence measures, the literature has not provided a satisfactory formulation for the case of intuitionistic fuzzy sets (IFS). This paper criticizes the existing attempts in terms of respect of the basic axioms of a divergence measure. Then, new improved, axiomatically supported divergence measures for IFSs are proposed. Additional properties of the new divergence measures are discussed to guarantee their good performance. Transformation relationships with entropy and dissimilarity measures are debated. As an application, a new intuitionistic fuzzy set theory-based ranking method for figure skaters is designed. A numerical example illustrates its applicability. It uses real data produced during the Men Single Skating Short Program performed in the Team Event in Figure Skating during the Olympic Winter Games 2018 PyeungChang held in Korea from 09.02.2018 to 25.02.2018.