Intra regular Abel-Grassmann's groupoids characterized by their intuitionistic fuzzy ideals

TL;DR

This paper explores the properties of intuitionistic fuzzy ideals in intra-regular AG-groupoids, providing characterizations and structural insights into these algebraic systems using fuzzy set theory.

Contribution

It introduces new characterizations of intra-regular AG-groupoids via intuitionistic fuzzy ideals and establishes the semilattice structure of their two-sided ideals.

Findings

Intra-regular AG-groupoids are characterized by their fuzzy ideals.

Fuzzy left, right, interior, and quasi ideals coincide in intra-regular AG-groupoids.

The set of fuzzy two-sided ideals forms a semilattice.

Abstract

In this paper, we have discussed the properties of intuitionistic fuzzy ideals of an AG-groupoids. We have characterized an intra-regular AG-groupoid in terms of intuitionistic fuzzy left (right, two-sided) ideals, fuzzy (generalized) bi-ideals, intuitionistic fuzzy interior ideals and intuitionistic fuzzy quasi ideals. We have proved that the intuitionistic fuzzy left (right, interior, quasi) ideal coincides in an intra-regular AG-groupoid. We have also shown that the set of intuitionistic fuzzy two-sided ideals of an intra-regular AG-groupoid forms a semilattice structure.