R. Khan - Department of Mathematics, Bach Khan University, Charsadda, KPK, Pakistan.
A. Khan - Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan.
B. Ahmad - Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan.
R. Gul - Department of Mathematics, Bach Khan University, Charsadda, KPK, Pakistan.

For 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.

Soft sets, N)-uni-soft ideal, (M, N)-uni-soft interior ideals