On fuzzy-Γ-ideals of Γ-Abel-Grassmann's groupoids

Abstract

In this paper, we have introduced the notion of Γ-fuzzification in Γ-AG-groupoids which is in fact the generalization of fuzzy AG-groupoids. We have studied several properties of an intra-regular Γ-AG^{**}-groupoids in terms of fuzzy Γ-left (right, two-sided, quasi, interior, generalized bi-, bi-) ideals. We have proved that all fuzzy Γ-ideals coincide in intra-regular Γ-AG^{**}-groupoids. We have also shown that the set of fuzzy Γ-two-sided ideals of an intra-regular Γ-AG^{**}-groupoid forms a semilattice structure.