Document Type : Original Article
The University of Haripur, KPK, Pakistan
Faculty of Engineering, Arab Academy for Science and Technology and Maritime Transport (AASTMT), Aswan Branch, Egypt
Department of Mathematics and Statistics, The University of Haripur, Haripur, KP, Pakistan
Higher Institute of Engineering and Technology King Marriott, P.O. Box 3135, Egypt
Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan
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.