Document Type: Regular Paper
Department of Mathematics, COMSATS Institute of Information Technology Khyber Pukhtoon Khwa, Abbottabad, Pakistan
Department of Mathematics, Faculty of Science, University of Technology, Malaysia 81310 UTM Johor Bahru, Johor, Malaysia
Department of Mathematics, Yazd University Yazd, Iran
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.