Generalized Hesitant Fuzzy Ideals in Semigroups

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.