Document Type : Original Article
Abdul Wali Khan University Mardan
Department of Mathematics, FATA University, Kohat, KP, Pakistan
Department of Mathematics Abdul Wali Khan University Mardan
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.