In this paper, we introduce the notions of interval-valued fuzzy prime (resp. strongly prime and semiprime) bi-ideals of a semigroup. By using these ideas we characterize those semigroups for which each interval-valued fuzzy bi-ideal is semiprime and strongly prime.

In this paper we characterize those hemirings for which each k-ideal is idempotent. We also characterize those hemirings for which each fuzzy k-ideal is idempotent. The space of prime k-ideals (fuzzy k-prime k-ideals) is topologized.

The notions of a S fuzzy ∧ sub semi lattice, a S fuzzy ideal and a S fuzzy prime ideal of a bounded lattice with truth values in a bounded ∧ sub semi lattice S are introduced which generalize the existing notions with truth values in a unit interval of real numbers. Finally, S fuzzy prime ideal theorem is proved. 2010 AMS Classification: 03G10, 46H10, 06D50, 08A72

The aim of this paper is to introduce the notion of anti fuzzy (prime) deductive system in BL-algebra and to investigate their properties. It is shown that the set of all deductive systems (with the empty set) of a BL-algebra X is equipotent to a quotient of the set of all anti fuzzy deductive systems of X. The anti fuzzy prime deductive system theorem of BL-algebras is also proved. Anti Fuzzy ...

In the formal and fully graded setting of Fuzzy Class Theory (or higher-order fuzzy logic) we make an initial investigation into basic notions of fuzzy topology. In particular we study graded notions of fuzzy topology regarded as a fuzzy system of open or closed fuzzy sets and as a fuzzy system of fuzzy neighborhoods. We show their basic graded properties and mutual relationships provable in Fu...

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...

*Correspondence: [email protected] School of Mathematics Science, Liaocheng University, Liaocheng, Shandong 252059, China Abstract In order to generalize the notions of a (∈,∈ ∨q)-fuzzy subring and various (∈,∈ ∨q)-fuzzy ideals of a ring, a (λ,μ)-fuzzy subring and a (λ,μ)-fuzzy ideal of a ring are defined. The concepts of (λ,μ)-fuzzy semiprime, prime, semiprimary and primary ideals are introdu...

Fuzzy logic is understood as a logic with a comparative and truth-functional notion of truth. Arithmetical complexity of sets of tautologies (identically true sentences) and satissable sentences (sentences true in at least one interpretation) as well of sets of provable formulas of the most important systems of fuzzy predicate logic is determined or at least estimated .

Department of Mathematics, Jadavpur University Kolkata-700032, India manasi−[email protected] Abstract The notion of intuitionistic fuzzy set was introduced by Atanassov as a generalization of the notion of fuzzy set. In this paper we apply this concept of Atanassov to ideals, prime ideals and semiprime ideals of Γsemigroups in order to obtain some characterization theorems. We also introduce the not...