Generalized Green's relations and GV-ordered semigroups

Ideals and Green's relations in ordered semigroups

Exactly as in semigroups, Green’s relations play an important role in the theory of ordered semigroups—especially for decompositions of such semigroups. In this paper we deal with the -trivial ordered semigroups which are defined via the Green’s relation , and with the nil and Δ-ordered semigroups. We prove that every nil ordered semigroup is -trivial which means that there is no ordered semigr...

GENERALIZED UNI-SOFT INTERIOR IDEALS IN ORDERED SEMIGROUPS

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 introduc...

Generalized fuzzy filters in ordered semigroups

Fuzzy semigroup theory concentrates on theoretical aspects, but also includes applications in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. In this paper, we introduce the concept of an ( , )-fuzzy filter of an ordered semigroup , where , , , , with . Since the concept of ( , )-fuzzy filter is an important and useful generalization of ordinary fuzzy filter,...

Generalized Intuitionistic Fuzzy Ideals of Ordered Semigroups

The notion of intuitionistic fuzzy ideals with thresholds of an ordered semigroup is considered and some of its properties are given. An embedding theorem of the set of all intuitionistic fuzzy ideals with thresholds is presented and the homomorphic images and inverse images of intuitionistic fuzzy ideals with thresholds are studied too. 2010 Mathematics Subject Classification: 06F05

Ordered Categories and Ordered Semigroups