In this paper we extend some results concerning ideals of left regular and intra-regular ordered semigroups to fuzzy ordered semigroups. A theory of fuzzy sets on ordered groupoids and ordered semigroups can be developed. Some results on ordered groupoidssemigroups have been already given by the same authors. The aim of writing this paper is to show the way we pass from the theory of ordered se...

Let S be an ordered semigroup. In this paper we first introduce the concepts of (∈,∈ ∨qk)-fuzzy ideals, (∈,∈ ∨qk)-fuzzy bi-ideals and (∈,∈ ∨qk)-fuzzy generalized bi-ideals of an ordered semigroup S by the ordered fuzzy points of S, and investigate their related properties. Furthermore, characterizations of regular ordered semigroups by the properties of (∈,∈ ∨qk)-fuzzy left ideals, (∈,∈ ∨qk)-fu...

in this paper, we introduce a considerable machinery which permits us to characterize a number of special (fuzzy) subsets in ag -groupoids. generalizing the concepts of (,q) -fuzzy bi-ideals (interior ideal), we define ( , ) k q -fuzzy bi-ideals, ( , ) k q -fuzzy left (right)-ideals and ( , ) k q -fuzzy interior ideals in ag -groupoids and discuss some fundamental aspects of these i...

Abstract. In this paper, we introduce generalized fuzzy weakly interior ideals of an ordered semigroup. We generalize fuzzy interior ideals of an ordered semigroup. We establish necessary and sufficient condition for a fuzzy set to be a generalized fuzzy weakly interior ideal. We establish three equivalent conditions for an ordered semigroup to be regular. We characterize semisimple ordered sem...

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 apply the biswas’ idea of anti fuzzy subgroups toideals of near-rings. we introduce the notion of anti fuzzy ideals of near-rings,and investigate some related properties.

In this note, we show that an ordered ternary semigroup is left and right simple if and only if it does not contain proper bi-ideals. The similar result is valid on ordered semigroups [7], on ordered Γ-semigroups [3] and on ternary semigroups [4]. Mathematics Subject Classification: 06F05

The notions of int-soft semigroups and int-soft left (resp., right) ideals in semigroups are studied in the paper by Song et al. (2014). In this paper, further properties and characterizations of int-soft left (right) ideals are studied, and the notion of int-soft (generalized) bi-ideals is introduced. Relations between int-soft generalized bi-ideals and int-soft semigroups are discussed, and c...

Throughout this paper, the ring R is not necessarily with an identity. We denote the set of all idempotents of R by E(R). Also, for a subset X ⊆ R, we denote the right (resp., left) annihilator of X in R by annr(X) (resp., ann (X)). Now, according to Fraser and Nicholson in [5], we call a ring R a left p.p.-ring, in brevity, l.p.p.-ring, if for all x ∈ R, there exists an idempotent e such that ...