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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.

Keywords

Ordered semigroups left/right regular and completely regular ordered semigroup quasi-ideal uni-soft quasi-ideal semiprime uni-soft quasi-ideal

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Applications of soft union sets in ordered semigroups via uni-soft quasi-ideals

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