On inf -Hesitant Fuzzy Γ -Ideals of Γ -Semigroups

Abstract

The notions of an $\inf$ -hesitant fuzzy $\mathrm{\Gamma }$ -ideal and a $\left(\sup ,\inf \right)$ -hesitant fuzzy $\mathrm{\Gamma }$ -ideal, which are a generalization of an interval-valued fuzzy $\mathrm{\Gamma }$ -ideal, of a $\mathrm{\Gamma }$ -semigroup are introduced and some properties are investigated. Characterizations of the notions are provided in terms of sets, fuzzy sets, intuitionistic fuzzy sets, interval-valued fuzzy sets, and hesitant fuzzy sets. Furthermore, characterizations of a $\mathrm{\Gamma }$ -ideal of a $\mathrm{\Gamma }$ -semigroup are given in terms of $\inf$ -hesitant and $\left(\sup ,\inf \right)$ -hesitant fuzzy $\mathrm{\Gamma }$ -ideals.