In this paper, we apply the concept of fuzzy soft sets to ordered semigroup theory. The concepts of (∈γ ,∈γ ∨qδ)-fuzzy left (right) ideals, (∈γ ,∈γ ∨qδ)-fuzzy biideals and (∈γ ,∈γ ∨qδ)-fuzzy quasi-ideals are introduced and some related properties are obtained. Three kinds of lattice structures of the set of all (∈γ ,∈γ ∨qδ)-fuzzy soft left (right) ideals of an ordered semigroup are derived. The...

In this paper, fuzzy h-bi-ideals, fuzzy h-quasi-ideals and fuzzy h-interior ideals of a Γ-hemiring are studied and some related properties are investigated. The notions of h-intra-hemiregularity and h-quasi-hemiregularity of a Γ-hemiring are introduced and studied along with h-hemiregularity and their characterizations in terms of fuzzy h-ideals are also obtained. The concept of fuzzy h-duo Γ-h...

In this paper we introduce the notion of intuitionistic fuzzy prime, strongly prime, semiprime bi-ideals in ternary semigroup and look for some of their related characteristics. Also here we introduce irreducible and strongly irreducible intuitionistic fuzzy bi-ideals in a ternary semigroup. AMS subject classification: 20N10, 20M12, 04A72.

We characterize the fuzzy bi-ideal generated by a fuzzy subset in a semigroup and the fuzzy bi-ideal generated by a fuzzy subset A such that A ⊆ A2 in a semigroup with an identity element. Our work generalizes the characterization of fuzzy bi-ideals by Mo and Wang ([8]).

On the basis of the concept of interval valued intuitionistic fuzzy set introduced by K. Atanassov [3], the notion of interval valued intuitionistic fuzzy subsemigroup (ideal, bi-ideal, (1, 2)-ideal) of a semigroup with respect to t-norm T and s-norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help o...

In this paper, we introduce a new sort of interval valued $left(in ,in vee q_{widetilde{k}}^{widetilde{delta }}right) $-fuzzy bi-ideal in ordered semigroups which is the generalization of interval valued $left( in ,in vee q_{%widetilde{k}}right) $-fuzzy bi-ideal and interval valued $left( in ,in vee qright) $-fuzzy bi-ideal of ordered semigroups. We give examples in which we show that these str...

In this paper we introduce the concept of fuzzy generalized bi-ideal of a Γsemigroup, which is an extension of the concept of a fuzzy bi-ideal of a Γsemigroup and characterize regular Γ-semigroups in terms of fuzzy generalized bi-ideals. AMS Mathematics Subject Classification(2000): 08A72, 20M12, 3F55

In this paper we have studied the concept of Anti fuzzy ideals in Left Almost Semigroups (LA-semigroup in short). The equivalent statement for an LA-semigroup to be a commutative semigroup is proved. The set of all anti fuzzy left ideals, which are idempotents, forms a commutative monoid. Moreover it has been shown that the union of any family of Anti fuzzy left ideals of an LA-semigroup is an ...

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...

Using the idea of a quasi-coincedence of a fuzzy point with a fuzzy set, the concept of an (α, β)-fuzzy bi-ideal in ordered semigroups is introduced, which is a generalization of the concept of a fuzzy bi-ideal in ordered semigroups and some interesting characterizations theorems are obtained. A special attention is given to (∈,∈ ∨q)-fuzzy bi-ideals. 2000 Mathematics Subject Classification: 06F...