Union Soft Set Theory Applied To Ordered Semigroups

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 delta-exclusive set is given and the relations between uni-soft bi-ideals and delta-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 delta-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.