Hesitant relations: Novel properties and applications in three-way decisions

Abstract

Since Torra introduced the concept of hesitant fuzzy sets, it has seen wide applications in decision-making problems, cluster analysis, medical diagnosis, personnel appraisal, information retrieval and so on. And, nowadays, there arise many discussions related to hesitant fuzzy sets. In particular, recently, Hu extends the truth values set of hesitant fuzzy sets and hesitant fuzzy relations from the family of subsets of unit interval to the family of nonempty subsets of any linearly ordered set with an involutive negator and calls them hesitant sets and hesitant relations, respectively. This paper continues to consider this topic and mainly intends to give a systematical discussion to hesitant relations on their properties and potential applications in three-way decisions. First, this paper shows some novel properties of the operations on linearly ordered set with an involutive negator. Second, this paper investigates some vital properties of hesitant relations, especially for the compositions, projections, reflexivity, symmetry, *-transitivity and so on. Third, this paper proposes various types of ordered hesitant relations. Finally, this paper discusses some applications of hesitant relations in the constructions of decision evaluation functions in three-way decision spaces.