Necessary and possible hesitant fuzzy sets: A novel model for group decision making

Abstract

We propose an extension of Torra’s notion of hesitant fuzzy set, which appears to be well suited to group decision making. In our model, indecisiveness in judgements is described by two nested hesitant fuzzy sets: the smaller, called necessary, collects membership values determined according to a rigid evaluation, whereas the larger, called possible, comprises socially acceptable membership values. We provide several instances of application of our methodology, and accordingly design suitable individual and group decision procedures. This novel approach displays structural similarities with Atanassov’s intuitionistic fuzzy set theory, but has rather different goals. Our source of inspiration comes from preference theory, where a bi-preference approach has proven to be a useful extension of the classical mono-preference modelization in the fields of decision theory and operations research.