Some Generalized Distance and Similarity Measures for Picture Hesitant Fuzzy Sets and Their Applications in Building Material Recognition and Multi-Attribute Decision Making

Abstract

The aim of this article is to develop some distance measures for newly defined framework of picture hesitant fuzzy set (PHFS). A PHFS is a picture fuzzy set (PFS) having membership, abstinence and non-membership grades in the form of hesitant fuzzy numbers (HFNs). These distance measures include generalized picture hesitant distance measure, generalized picture hesitant normalizer distance measure, generalized picture hesitant weighted distance measure and generalized picture hesitant normalizer weighted distance measure along with some other distance measures. A comparison of developed distance measures is established with existing distance measures and their advantages are discussed.