Γ-Abel-Grassmann's groupoids characterized by their intuitionistic Γ-ideals

Abstract

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