Novel Distance Measures of Picture Fuzzy Sets and Their Applications

Picture fuzzy sets (PFSs), as a generalization of traditional fuzzy sets and intuitionistic fuzzy sets (IFSs), offer a powerful framework for modeling and dealing with imprecise and uncertain information and have been widely used in various fields. Nevertheless, how to effectively measure the differences or similarities between PFSs is still a challenging and urgent problem. Despite that some distance measures for PFSs have been developed, some of them have counterintuitive and unreasonable results and even partially fail to satisfy the axiomatic definition of distance measures. To handle these limitations, in this paper, we propose two distance measures of PFSs motivated by the merits of Jensen–Shannon divergence. Specifically, the first distance measure of the PFSs considers the positive degree, neutral degree and negative degree. The second distance measure introduces the refusal degree on this basis. Moreover, the proposed distance measures not only satisfy the axiomatic definition but also overcome the counterintuitive results of existing distance measures. Finally, two kinds of applications related to pattern recognition and medical diagnosis are used to verify the performance of the proposed distance measures.