Affiliations: [a] Department of Mathematics, Garden Campus, Abdul Wali Khan University, Mardan KPK, Pakistan | [b] Department of Mathematics Education and RINS, Gyeongsang National University, Chinju, Korea | [c] Department of Mathematics, Islamia College University, Peshawar, KPK, Pakistan
Correspondence:
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Corresponding author. Asghar Khan, Department of Mathematics, Garden Campus, Abdul Wali Khan University, Mardan KPK, Pakistan. Tel.: +92 337 575757; E-mail: [email protected].
Abstract: Molodtsov in 1999, introduced the concept of a soft set as a new mathematical tool which can be seen as a new approach to deal with uncertainty and vagueness in information systems. Using the notion of soft-union sets in ordered semigroup, we characterize ordered semigroups in terms of union-soft (uni-soft) quasi-ideals. We characterize left, right simple and completely regular ordered semigroups in terms of uni-soft quasi-ideals. We define semiprime uni-soft quasi-ideal of ordered semigroups and characterize completely regular ordered semigroup in terms of semiprime uni-soft quasi-ideals. We also study the decomposition of left and right simple ordered semigroups having special property, by means of uni-soft quasi-ideals.
