Characterization of ordered semihypergroups in terms of uni-soft bi-hyperideals

In this paper, we introduce the concept of unionsoft (briefly, uni-soft) bi-hyperideal of an ordered semihypergroup. The notions of prime (strongly prime, semiprime, irreducible, and strongly irreducible) uni-soft bi-hyperideals in ordered semihypergroups are introduced and related properties are investigated. Numerous examples of these notions are given. The relationship between prime and strongly prime, irreducible and strongly irreducible uni-soft bi-hyperideals are considered and characterizations of these concepts are established. Regular and intra-regular ordered semihypergroups are characterized in terms of these notions.