Abstract
In this paper, as a generalization of the concepts of hesitant fuzzy bi-ideals and hesitant fuzzy right (resp. left) ideals of semigroups, the concepts of hesitant fuzzy m , n -ideals and hesitant fuzzy m , 0 -ideals (resp. 0 , n -ideals) are introduced. Furthermore, conditions for a hesitant fuzzy m , n -ideal ( m , 0 -ideal, 0 , n -ideal) to be a hesitant fuzzy bi-ideal (right ideal, left ideal) are provided. Moreover, several correspondences between bi-ideals (right ideals, left ideals) and hesitant fuzzy m , n -ideals ( m , 0 -ideals, 0 , n -ideals) are obtained. Also, the characterizations of different classes of semigroups in terms of their hesitant fuzzy m , n -ideals and hesitant fuzzy m , 0 -ideals ( 0 , n -ideals) are investigated.
Highlights
Torra [1] defined hesitant fuzzy sets in terms of a function that returns a set of membership values for each element in the domain. e hesitant fuzzy set offers a more accurate representation of hesitancy among people in expressing their preferences over objects than the fuzzy set or its classical extensions. is is really helpful to express the hesitancy of people in everyday life. e hesitant fuzzy set is a valuable tool to deal with uncertainty, which can be accurately and ideally described in terms of decision makers’ opinions
Torra [1] defined hesitant fuzzy sets as a function returning a collection of membership values for each domain element. e hesitant fuzzy set offers a more accurate representation of hesitancy among people in expressing their preferences over objects than the fuzzy set or its classical extensions
Hesitant fuzzy set theory was applied to many practical problems, in the field of decision-making
Summary
Received 6 September 2020; Accepted 17 November 2020; Published 22 December 2020. In this paper, as a generalization of the concepts of hesitant fuzzy bi-ideals and hesitant fuzzy right (resp. left) ideals of semigroups, the concepts of hesitant fuzzy (m, n)-ideals and hesitant fuzzy (m, 0)-ideals (resp. (0, n)-ideals) are introduced. The characterizations of different classes of semigroups in terms of their hesitant fuzzy (m, n)-ideals and hesitant fuzzy (m, 0)-ideals ((0, n)-ideals) are investigated. As a new generalization of fuzzy sets, Torra [1] introduced the notion of hesitant fuzzy sets which permit the membership degree of an element to a set to be represented by a set of possible values between 0 and 1 (see [1, 2]). Motivated by a lot of work on hesitant fuzzy sets, we introduce the notions of hesitant fuzzy (m, n)-ideals, hesitant fuzzy (m, 0)-ideals, and hesitant fuzzy (0, n)-ideals of a semigroup by generalizing the concept of hesitant fuzzy bi-ideals, hesitant fuzzy right ideals, and hesitant fuzzy left ideals. Characterizations of different semigroup classes such as (m, n)-regular, (m, 0)-regular, and (0, n)-regular semigroups in terms of their hesitant fuzzy (m, n)-ideals, hesitant fuzzy (m, 0)-ideals, and hesitant fuzzy (0, n)-ideals are given
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