{\Gamma}-Abel-Grassmann's groupoids characterized by their intuitionistic {\Gamma}-ideals

TL;DR

This paper explores properties of intuitionistic fuzzy {\Gamma}-ideals in {\Gamma}-AG-groupoids, characterizing intra-regular structures and showing the equivalence and lattice structure of various ideals.

Contribution

It introduces a comprehensive characterization of intra-regular {\Gamma}-AG^{**}-groupoids using intuitionistic fuzzy {\Gamma}-ideals and establishes their algebraic structure.

Findings

Intuitionistic fuzzy {\Gamma}-left, right, interior, and quasi-ideals coincide in intra-regular {\Gamma}-AG^{**}-groupoids.

The set of two-sided ideals forms a semilattice.

Characterization of intra-regular {\Gamma}-AG^{**}-groupoids via fuzzy ideals.

Abstract

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