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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.

Keywords

DFS set regular AG-groupoid choice values DFS-weighted set

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( M,N )-Double framed soft ideals of Abel Grassmann’s groupoids

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