Picture Hesitant Fuzzy Clustering Based on Generalized Picture Hesitant Fuzzy Distance Measures

Abstract

Certain scholars have generalized the theory of fuzzy set, but the theory of picture hesitant fuzzy set (PHFS) has received massive attention from distinguished scholars. PHFS is the combination of picture fuzzy set (PFS) and hesitant fuzzy set (HFS) to cope with awkward and complicated information in real-life issues. The well-known characteristic of PHFS is that the sum of the maximum of the membership, abstinence, and non-membership degree is limited to the unit interval. This manuscript aims to develop some generalized picture hesitant distance measures (GPHDMs) as a generalization of generalized picture distance measures (GPDMs). The properties of developed distance measures are investigated, and the generalization of developed theory is proved with the help of some remarks and examples. A clustering problem is solved using GPHDMs and the results obtained are explored. Some advantages of the proposed work are discussed, and some concluding remarks based on the summary of the proposed work and as well as future directions, are added.