Hesitant fuzzy sets and hesitant fuzzy relations with membership values in power set quantales

Document Type : Original Manuscript

Authors

1 Department of Sciences, Mathematics and Technical Sciences, Pedagogical Faculty in Vranje, University of Niš, Vranje, Serbia

2 Department of Computer Science, Faculty of Science and Mathematics, University of Niš, Niš, Serbia

Abstract

A hesitant fuzzy set extends the notion of a fuzzy set by allowing membership values to be represented as sets of values drawn from a predefined domain, typically the real unit interval. In this paper, we introduce a novel framework in which membership values are instead drawn from the power set quantale of a semigroup. This shift is motivated by the fact that such a power set quantale admits residuation, thereby offering a rich algebraic setting for the development of the theory of hesitant fuzzy sets and hesitant fuzzy relations. We provide several characterizations of hesitant fuzzy relations, with particular emphasis on hesitant fuzzy equivalences, their classes and partitions, as well as hesitant fuzzy quasi-orders.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 23, Issue 6
November and December 2026
Pages 67-98

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