An (α,β)Hesitant Fuzzy Set Approach to Ideal Theory in Semigroups
Abstract
The aim of this manuscript is to introduce the \((\alpha,\beta)\)hesitant fuzzy set and apply it to semigroups. In this paper, as a generalization of the concept of hesitant fuzzy sets to semigroup theory, the concept of \((\alpha,\beta)\)hesitant fuzzy subsemigroups of semigroups is introduced, and related properties are discussed. Furthermore, we define and study \((\alpha,\beta)\)hesitant fuzzy ideals on semigroups. In particular, we investigate the structure of \((\alpha,\beta)\)hesitant fuzzy ideal generated by a hesitant fuzzy ideal in a semigroup. In addition, we also introduce the concepts of \((\alpha,\beta)\)hesitant fuzzy semiprime sets of semigroups, and characterize regular semigroups in terms of \((\alpha,\beta)\)hesitant fuzzy left ideals and \((\alpha,\beta)\)hesitant fuzzy right ideals. Finally, several characterizations of regular and intraregular semigroups by the properties of \((\alpha,\beta)\)hesitant ideals are given.
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