Characterizations of regularities in ordered semihypergroups in terms of some generalized union soft hyperideals

Abstract

A soft set of \(E\) over \(U\) is a mapping from \(E\) to the set of all subsets of \(U\). There are many studies that apply the concept of soft sets to investigate the properties of some algebraic structures. The notions of \((M, N)\)-union soft left (resp., right) hyperideals in ordered semihypergroups were introduced by Farooq, Khalaf, and Khan. These concepts are generalizations of uni-soft left and right hyperideals. Ordered semihypergroups can be characterized by many mathematical concepts, such as their hyperideals, fuzzy hyperideals, and soft hyperideals. In this paper, we apply the notions of \((M, N)\)-union soft left (resp., right) hyperideals to characterize some regularities of ordered semihypergroups: regular, weakly regular, and intra-regular ordered semihypergroups.