On fuzzy-{\Gamma}-ideals of {\Gamma}-Abel-Grassmann's groupoids

TL;DR

This paper introduces fuzzy-{\Gamma}-ideals in {\Gamma}-AG-groupoids, generalizing fuzzy AG-groupoids, and explores their properties in intra-regular {\Gamma}-AG^{**}-groupoids, revealing that all fuzzy {\Gamma}-ideals coincide and form a semilattice.

Contribution

It generalizes fuzzy AG-groupoids to {\Gamma}-AG-groupoids and studies their ideal structures in intra-regular cases, showing all fuzzy {\Gamma}-ideals coincide and form a semilattice.

Findings

All fuzzy {\Gamma}-ideals coincide in intra-regular {\Gamma}-AG^{**}-groupoids.

The set of fuzzy {\Gamma}-two-sided ideals forms a semilattice.

Properties of various fuzzy {\Gamma}-ideals are characterized in intra-regular {\Gamma}-AG^{**}-groupoids.

Abstract

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