Union soft set theory applied to ordered semigroups

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Raees Khan
Asghar Khan
Muhammad Uzair Khan
Nasir Khan

Abstract

The uni-soft type of bi-ideals in ordered semigroup is considered. The notion of a uni-soft bi-ideal is introduced and the related properties are investigated. The concept of δ-exclusive set is given and the relations between uni-soft bi-ideals and δ-exclusive set are discussed. The concepts of two types of prime uni-soft bi-ideals of an ordered semigroup S are given and it is proved that, a non-constant uni-soft bi-ideal of S is prime in the second sense if and only if each of its proper δ-exclusive set is a prime bi-ideal of S. The characterizations of left and right simple ordered semigroups are considered. Using the notion of uni-soft bi-ideals, some semilattices of left and right simple semigroups are provided. By using the properties of uni-soft bi-ideals, the characterization of a regular ordered semigroup is provided. In the last section of this paper, the characterizations of both regular and intra-regular ordered semigroups are provided.

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