In this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy bi-ideals of a semigroup. We characterize thosesemigroups for which each fuzzy bi-ideal is semiprime. We also characterizethose semigroups for which each fuzzy bi-ideal is strongly prime.

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]).

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 ...

There are two equivalent de nitions of a fuzzy right ideal, fuzzy left ideal, fuzzy bi-ideal or fuzzy quasi-ideal f of an ordered semigroup (or a semigroup) S in the bibliography. The rst one is based on the fuzzy subset f itself, the other on the multiplication of fuzzy sets and the greatest fuzzy subset of S. Investigations in the existing bibliography are based on the rst de nition. The pres...

In this paper we have introduced fuzzy quasi-ideal and fuzzy left(right, two-sided) ideals in LA-semigroup. We have proved some results related to fuzzy quasi-ideals and fuzzy left(right, two-sided) ideals of an LA-semigroup. Further we characterize an intra-regular LA-semigroup by the properties of their fuzzy ideals.

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 the concept of Q-fuzzification of ideals of Γ-semigroups has been introduced and some important properties have been investigated. A characterization of regular Γ-semigroup in terms of Q-fuzzy ideals has been obtained. Operator semigroups of a Γ-semigroup has been made to work by obtaining various relationships between Q-fuzzy ideals of a Γ-semigroup and that of its operator semig...

Our aim in this paper is to introduce and study a new sort of fuzzy ternary subsemigroup (left ideal, right ideal, lateral ideal, quasi-ideal, bi-ideal) of a ternary semigroup, called interval-valued (α,β )-fuzzy ternary subsemigroup (left ideal, right ideal, lateral ideal, quasi-ideal, bi-ideal). We also characterize regular ternary semigroups in terms of these interval-valued fuzzy ideals.

The intuitionistic fuzzification of the notion of a bi-ideal in ordered semigroups is considered. In terms of intuitionistic fuzzy set, conditions for an ordered semigroup to be completely regular is provided. Characterizations of intuitionistic fuzzy bi-ideals in ordered semigroups are given. Using a collection of bi-ideals with additional conditions, an intuitionistic fuzzy bi-ideal is constr...

Our aim in this paper is to introduce the notion of fuzzy soft near-subtraction semigroups and fuzzy soft ideals of near-subtraction semigroups. We discuss some important properties of these new fuzzy algebraic structure and investigate some examples and counter examples.