Hesitant fuzzy sets and relations using lists

Abstract

Hesitant Fuzzy Sets are useful to represent the information given by several experts. However, this possibility usually require to deal with sets of values with different cardinality and the necessity to compare them, it is, not all experts evaluate all the elements in the universe. In this paper it is proposed a new nomenclature for Hesitant Fuzzy Sets called Hesitant Fuzzy Sets using Lists. It is proposed a new partial order relation between lists of membership degrees. This partial order relation allows to handle lists with different lengths. In addition, Hesitant Fuzzy Relations on Lists operations are defined and the T-transitive closure of a Hesitant Fuzzy Relation is given. It is proved this T-transitive closure always exists and it is unique. Finally, an algorithm to compute the T-transitive closure of a Hesitant Fuzzy Relation is proposed and several examples are given.