In this paper we define intuitionistic fuzzy quasi-ideals of ordered semigroups. The main result of the paper is a characterization of quasi-ideals in terms of intuitionistic fuzzy quasi-ideals. We also characterize left simple, right simple, and completely regular ordered semigroups in terms of intuitionistic fuzzy quasi-ideals. We study the decomposition of left and right simple ordered semig...

It is well known that the right (left) regular, regular, and intra-regular ordered semigroups play an essential role in studying the structure, especially the decomposition, of ordered semigroups. In the present paper we study some more general classes containing the right regular, left regular, regular and intra-regular ordered semigroups. As an application of our results we get characterizati...

In this paper, we present the concepts of a fuzzy soft left (right) ideal and fuzzy soft interior ideal over an ordered semigroup S . Some basic results of fuzzy soft left (right) ideals and fuzzy soft interior ideals are investigated and the supported examples are provided. Different classes, regular, intra-regular, and simple ordered semigroups are characterized by means of fuzzy soft left (r...

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...

In this paper, we endow set S with the structure of an ordered semigroup and define “intuitionistic fuzzy” analogous for several notions that have been proved to be useful in the theory of ordered semigroups and give some equivalent conditions of these definitions. Then we characterize the completely regular and the strongly regular ordered semigroups by means of intuitionistic fuzzy bi-ideals.

This paper consider the   general  forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. Special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related  pr...

In this paper an extensive study of the concepts generalized Green’s relations and GV -semigroups without order to ordered semigroups have been given. Our approach allows one see nature in class -ordered semigroups. Moreover we show that semigroup S is a if only complete semilattice completely π-regular Archimedean