Regular AG-groupoids characterized by ( , ) k q -fuzzy ideals

Abstract

In this paper, we introduce a considerable machinery which permits us to characterize a number of special (fuzzy) subsets in AG -groupoids. Generalizing the concepts of (,q) -fuzzy bi-ideals (interior ideal), we define ( , ) k q -fuzzy bi-ideals, ( , ) k q -fuzzy left (right)-ideals and ( , ) k q -fuzzy interior ideals in AG -groupoids and discuss some fundamental aspects of these ideals in AG -groupoids. We further define ( , ) k  q -fuzzy bi-ideals and ( , ) k  q -fuzzy interior ideals and give some of their basic properties in AG -groupoids. In the last section, we define lower/upper parts of ( , ) k q -fuzzy left (resp. right) ideals and investigate some characterizations of regular and intera-regular AG -groupoids in terms of the lower parts of ( , ) k q -fuzzy left (resp. right) ideals and ( , ) k q -fuzzy bi-ideal of AG -groupoids.