Affiliations: [a] Department of Mathematics, Abdul Wali Khan University, Mardan, KP, Pakistan
| [b] Department of Electronics & Engineering, University of Engineering and Technology, Taxila, Sub Campus Chakwal, Pakistan
Correspondence:
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Correspondence to: Muhammad Izhar, Department of Mathematics, Abdul Wali Khan University, Mardan, KP, PAKISTAN. Ph: +923005744389; E-mail: mizharmath@gmail.com.
Abstract: The main motivation behind this paper is to study some structural properties of a non-associative structure Abel Grassmann’s groupoid (AG-groupoid) in terms of double-framed soft sets (DFS sets) as it hasn’t attracted much attention compared to associative structures. An AG-groupoid can be referred to as a non-associative semigroup, as the main difference between a semigroup and an AG-groupoid is the switching of an associative law. In this paper, we introduce the concept of (M, N)-double-framed soft ideals (briefly, (M, N)-DFS ideal) of AG-groupoids and investigate some properties of these notions. We have shown that every (M, N)-DFS ideal is (M, N)-DFS AG-groupoid but the converse is not true. This is shown with the help of an example. We also discuss the properties of (M, N)-DFS ideals in regular AG-groupoids. Moreover a decision making algorithm based on DFS-sets is given.
