Affiliations: [a] Department of Mathematics, Abdul Wali Khan University Mardan, KP, Pakistan
| [b] Higher Institute of Engineering and Technology, King Marioutt, Egypt; Department of Mathematics, Faculty of Science in Zulfi, Majmaah University, Zulfi, Saudi Arabia
Correspondence:
[*]
Corresponding author. Asghar Khan, Department of Mathematics, Abdul Wali Khan University Mardan, 23200 KP, Pakistan. Tel.: +923315479017; E-mail: azhar4set@yahoo.com.
Abstract: In order to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties, the notion of doubleframed soft set is introduced and applications in LA-semigroups are discussed. Double-framed soft set is a generalization of the theory of union and intersectional soft sets. In this article, we introduce the concept of double-framed soft set in LA-semigroups and study double-framed soft LA-semigroups (resp., left, right or two-sided) ideals (briefly, DFS left (right), DFS two-sided, and DFS bi-) ideals of an LA-semigroup S over an initial universe set U. The respective examples of these notions are investigated and the related properties are discussed. The basic properties of these notions are studied and characterizations of these concepts are discussed in detail.
Keywords: DFS-sets, DFS LA-semigroups, DFS ideals, DFS-set product, uni-int DFS-sets, DFS including set
