In this paper, we apply the concept of double-framed soft set (briefly DFS-set) to non-associative and non-commutative structure called Abel Grassmann’s groupoid (briefly AG-groupoid). We define double-framed soft quasi-ideals (briefly DFS quasi-ideal) of AG-groupoids and discuss their properties in left regular AG-groupoids. We also characterize left regular AG-groupoids in terms of DFS quasi-ideals. Application of DFS sets in decision making situation is provided.
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