Characterizations of Abel-Grassmann's groupoids by their intuitionistic fuzzy ideals

TL;DR

This paper explores the properties of AG-groupoids through the lens of intuitionistic fuzzy ideals, providing characterizations of regularity and intra-regularity and revealing structural insights.

Contribution

It introduces the concept of intuitionistic fuzzy ideals in AG-groupoids and characterizes their regularity properties using these fuzzy ideals, which is a novel approach.

Findings

All intuitionistic fuzzy ideals coincide in regular and intra-regular AG-groupoids.

The set of intuitionistic fuzzy two-sided ideals in a regular AG-groupoid forms a semilattice.

Conditions are provided for an AG-groupoid to be intra-regular based on fuzzy ideals.

Abstract

In this paper, we have introduced the concept of intuitionistic fuzzy ideals in an AG-groupoids. We have characterized regular and intra-regular AG-groupoids in terms of intuitionistic fuzzy left (right, two-sided) ideals, fuzzy (generalized) bi-ideals and intuitionistic fuzzy (1,2)-ideals. We have proved that all the intuitionistic fuzzy ideals coincides in regular and intra-regular AG-groupoids. It has been shown that the set of intuitionistic fuzzy two sided ideals of a regular AG-groupoid forms a semilattice structure. We have also given some useful conditions for an AG-groupoid to become an intra-regular AG-groupoid in terms their intuitionistic fuzzy ideals.