Affiliations: [a] Department of Mathematics, Abdul Wali Khan University Mardan, KP, Pakistan
| [b] Department of Mathematics, Yazd University, Yazd, Iran
Correspondence:
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Corresponding author. Asghar Khan, Department of Mathematics, Abdul Wali Khan University Mardan 23200, KP, Pakistan. Tel.: +923315479017; E-mail: asghar@awkum.edu.pk.
Abstract: Molodtsov soft set theory provides a general mathematical framework for dealing with uncertainty. The aim of this paper is to lay a foundation for providing a new soft algebraic tool in considering many problems that contain uncertainties. In order to provide these new soft algebraic structures, we introduce the notions of (M, N)-intersectional soft hyperideals and (M, N)-intersectional soft interior hyperideals of ordered semihypergroups. The concepts of (M, N)-intersectional soft hyperideals and (M, N)-intersectional soft interior hyperideals coincide in a regular as well as in intra-regular ordered semihypergroups. We introduce the notion of (M, N)-intersectional soft simple ordered semihypergroups. Furthermore we characterize (M, N)-intersectional soft simple ordered semihypergroups by means of (M, N)-intersectional soft hyperideals and (M, N)-intersectional soft interior hyperideals.
