Prime double-framed soft bi-ideals of ordered semigroup

The notions of a prime (strongly prime, semiprime, irreducible, and strongly irreducible) double-framed soft bi-ideals (briefly, prime, (strongly prime, semiprime, irreducible and strongly irreducible) DFS bi-ideals) in ordered semigroups are introduced and related properties are investigated. Several examples of these notions are provided. The relationship between prime and strongly prime, irreducible and strongly irreducible DFS bi-ideals are considered and  haracterizations of these concepts are established. The Characterizations of regular and intraregular ordered semigroups in terms of these notions are studied.