On (M,N) -intersectional soft interior hyperideals of ordered semihypergroups

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.