Regular ag-groupoids characterized by (∈, ∈ ∨ q k)-fuzzy ideals

• Main Authors: Khan, A., Sarmin, N. H., Khan, F. M., Davvaz, B.
• Format: Article
• Language: English
• Published: 2012
• Subjects: T Technology
• Online Access: http://eprints.utm.my/id/eprint/47460/1/NorHanizaSarmin2012_RegularAGgroupoidsCharacterized.pdf; http://eprints.utm.my/id/eprint/47460/

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 (∈, ∈ ∨ q k) -fuzzy bi-ideals, (∈, ∈ ∨ q k )-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 ( ∈, ∈ ∨ q k) -fuzzy bi-ideals and (∈, ∈ ∨ q k)-fuzzy interior ideals and give some of their basic properties in AG -groupoids. In the last section, we define lower/upper parts of (∈, ∈ ∨ q k ) -fuzzy left (resp. right) ideals and investigate some characterizations of regular and intera-regular AG -groupoids in terms of the lower parts of ( ∈, ∈ ∨ q k ) -fuzzy left (resp. right) ideals and ( ∈, ∈ ∨ q k )-fuzzy bi-ideal of AG -groupoids.