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 $\left(m,n\right)$ -ideals and hesitant fuzzy $\left(m,0\right)$ -ideals (resp. $\left(0,n\right)$ -ideals) are introduced. Furthermore, conditions for a hesitant fuzzy $\left(m,n\right)$ -ideal ( $\left(m,0\right)$ -ideal, $\left(0,n\right)$ -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 $\left(m,n\right)$ -ideals ( $\left(m,0\right)$ -ideals, $\left(0,n\right)$ -ideals) are obtained. Also, the characterizations of different classes of semigroups in terms of their hesitant fuzzy $\left(m,n\right)$ -ideals and hesitant fuzzy $\left(m,0\right)$ -ideals ( $\left(0,n\right)$ -ideals) are investigated.