Shahrood University of TechnologyJournal of Algebraic Systems2345-51287120190901GENERALIZED UNI-SOFT INTERIOR IDEALS IN ORDERED SEMIGROUPS6982144010.22044/jas.2018.6240.1310ENR. KhanDepartment of Mathematics, Bach Khan University, Charsadda, KPK, Pakistan.A. KhanDepartment of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan.B. AhmadDepartment of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan.R. GulDepartment of Mathematics, Bach Khan University, Charsadda, KPK, Pakistan.Journal Article20170921For all M,N∈P(U) such that M⊂N, we first introduced the definitions of (M,N)-uni-soft ideals and (M,N)-uni-soft interior ideals of an ordered semigroup and studied them. When M=∅ and N=U, we meet the ordinary soft ones. Then we proved that in regular and in intra-regular ordered semigroups the concept of (M,N)-uni-soft ideals and the (M,N)-uni-soft interior ideals coincide. Finally, we introduced (M,N)-uni-soft simple ordered semigroup and characterized the simple ordered semigroups in terms of (M,N)-uni-soft interior ideals.http://jas.shahroodut.ac.ir/article_1440_9fb818b35cb4a812855afbc3bd816fd1.pdf