Abel-Grassmann's groupoids characterized by (\in ,\in \vee q_{k}) fuzzy bi-ideals

TL;DR

This paper introduces and characterizes ({},{})-fuzzy bi-ideals in Abel-Grassmann's groupoids, generalizing existing fuzzy bi-ideals and providing new theoretical insights.

Contribution

It defines a new class of fuzzy bi-ideals in AG-groupoids using quasi-coincidence concepts, extending previous fuzzy ideal theories.

Findings

Characterization theorems for ({},{})-fuzzy bi-ideals

Generalization of fuzzy bi-ideals in AG-groupoids

New theoretical framework for fuzzy algebraic structures

Abstract

Using the idea of a quasi-coincedece of a fuzzy point with a fuzzy set, the concept of an ({\alpha},{\beta})-fuzzy bi-ibeals in AG-groupoid is introduced in this paper, which is a generalization of the concept of a fuzzy bi-ideal in AG-groupoid and some interesting characterizations theorems are obtained.