More Generalization of Union Soft Hyperideals of Ordered Semihypergroups

Abstract

In this paper, we introduce the notions of (M,N)-union soft hyperideals and (M,N)-union soft interior hyperideals of ordered semihypergroups. Some basic operations are investigated and some related properties are also studied. We present characterizations of ordered semihypergroups in terms of (M,N)-union soft hyperideals and (M,N)-union soft interior hyperideals. We prove that every (M,N)union soft hyperideal is an (M,N)-union soft interior hyperideal but the converse is not true which is shown with help of an example. However we show that the notions of (M,N)-union soft hyperideals and (M,N)-union soft interior hyperideals coincide in a regular as well as in intra-regular ordered semihypergroups. Moreover we introduce the notion of (M,N)-union soft simple ordered semihypergroups. Finally, we characterize (M,N)-union soft simple ordered semihypergroups by means of (M,N)-union soft hyperideals and (M,N)-union soft interior hyperideals.