A pseudo-addition in BL-algebras is a binary operation that is associative and non commutative. The aim of this paper is to use the notion of pseudo-addition to study the notion of ideal and fuzzy ideal as a natural generalization of that of ideal and fuzzy ideal in MV-algebras. Using a pseudo-addition, we characterize fuzzy ideals and also obtain a concrete description of the fuzzy ideals gene...

The fundamental concept of a fuzzy set, introduced by Zadeh in his classic paper [5] of 1965, has been applied by many authors to generalize some of the basic notions of algebra. In this note we characterize the semigroups for which each fuzzy ideal is prime, also the semigroups for which each fuzzy right ideal is prime. In Section 2, we prove that a semigroup is fully fuzzy prime if and only i...

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...

We consider the intuitionistic fuzzification of the concept of prime ideals in commutative BCK-algebras, and investigate some of their properties. We show that if P is a prime ideal of commutative BCK-algebra X iff ∼ P = 〈XP , − XP 〉 is an intuitionistic fuzzy prime ideal of X. We also prove that An IFS A = 〈μA, λA〉 of commutative BCK-algebra X is an intuitionistic fuzzy prime ideal of X if and...

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...