On algebraic properties of DFS sets and its application in decision making problems

Article type: Research Article

Authors: Khan, Asghar^a | Izhar, Muhammad^a | Hila, Kostaq^{b; *}

Affiliations: [a] Department of Mathematics, Abdul Wali Khan University, Mardan, KP, Pakistan | [b] Department of Mathematical Engineering, Polytechnic University of Tirana, Albania

Correspondence: [*] Corresponding author. Kostaq Hila, Department of Mathematical Engineering, Polytechnic University of Tirana, Albania. E-mail: kostaq_hila@yahoo.com.

Abstract: 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.

Keywords: DFS-set, DFS AG-groupoid, DFS int-uni product, DFS quasi-ideals, Left regular AG-groupoids, Decision making

DOI: 10.3233/JIFS-182572

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 6, pp. 6265-6281, 2019