Let S be an ordered semigroup. In this paper we first introduce the concepts of (∈,∈ ∨q)-fuzzy ideals, (∈,∈ ∨q)-fuzzy bi-ideals and (∈,∈ ∨q)-fuzzy generalized bi-ideals of an ordered semigroup S, and investigate their related properties. Furthermore, we also define the upper and lower parts of fuzzy subsets of an ordered semigroup S, and investigate the properties of (∈,∈ ∨q)-fuzzy ideals of S....

We introduce the notions of anti fuzzy right ideal, anti fuzzy right k-ideal and intuitionistic fuzzy right k-ideal of semirings. We investigate the their properties and connections with right k-ideal, fuzzy right k-ideal, anti fuzzy right k-ideal. We characterize regular semiring through intuitionistic fuzzy right ideal. The semi regularity of semirings is characterized by intuitionistic fuzzy...

The concept of (∈,∈∨ q)-fuzzy h-ideals of hemirings is introduced and some characterizations are described. We show that a hemiring S is hhemiregular if and only if for any (∈,∈∨ q)-fuzzy right h-ideal F and (∈,∈∨ q)fuzzy left h-ideal G, F ◦0.5 G = F ∩0.5 G. Finally, the concept of implicationbased fuzzy h-ideals of hemirings is considered. 2010 Mathematics Subject Classification: 16Y60, 13E05,...

In this paper, we first introduce the new concept of completely semiprime fuzzy ideals of an ordered semigroup S, which is an extension of completely semiprime ideals of ordered semigroup S, and investigate some its related properties. Especially, we characterize an ordered semigroup that is a semilattice of simple ordered semigroups in terms of completely semiprime fuzzy ideals of ordered semi...

In this paper we have defined anti fuzzy interior ideal in semigroups. We characterize regular, intra-regular and left (right) quasi-regular semigroups by the properties of their anti fuzzy ideals, anti fuzzy bi-ideals, anti fuzzy generalized bi-ideals, anti fuzzy interior ideals and anti fuzzy quasi-ideals.

In this paper, we characterize ordered semigroups in terms of fuzzy quasi-ideals. We characterize left simple, right simple and completely regular ordered semigroups in terms of fuzzy quasi-ideals. We define semiprime fuzzy quasi-ideal of ordered semigroups and characterize completely regular ordered semigroup in terms of semiprime fuzzy quasi-ideals. We also study the decomposition of left and...

If one of the axioms in ring, namely inverse axiom addition operation, is omitted, it will produce another algebraic structure, a semiring. Analogous to there are zero elements, ideal (left/right) semiring, and cross product semiring ideal. The analog fuzzy has (left/right), associated with membership value. This paper discuss cross-product two (more) ideals from Furthermore, always be But conv...

In this paper we introduce bipolar fuzzy subsemigroup, bipolar fuzzy left (right) ideals and bipolar fuzzy bi-ideal in ordered semigroups. We characterize different classes of ordered semigroups by the properties of their bipolar fuzzy ideals and bipolar fuzzy bi-ideals.

In this paper, we introduce the notion of fuzzy ideal,fuzzy weak ideal,fuzzy weakly prime left ideal and fuzzy prime left ideal system of a near-subtraction semigroup. We characterize fuzzy weak ideal and fuzzy ideal of a near-subtraction semigroup X through weak ideal and ideal of X respectively. We have shown that a fuzzy left ideal μ of a nearsubtraction semigroup X is a fuzzy weakly prime l...