The notion of fuzzy s-prime filters of a bounded BCK-algebra is introduced.We discuss the relation between fuzzy s-prime filters and fuzzy prime filters. By the fuzzy s-prime filters of a bounded commutative BCK-algebra X, we establish a fuzzy topological structure on X. We prove that the set of all fuzzy s-prime filters of a bounded commutative BCK-algebra forms a topological space. Moreover, ...

Pseudo-BCK algebras were introduced by G. Georgescu and A. Iorgulescu as a generalization of BCK algebras. Their properties and connections with other fuzzy structures were established by A. Iorgulescu and J. Kühr. In this paper we study the class of perfect pseudo-BCK algebras with pseudo-product and we prove that any perfect pseudo-BCK algebra with pseudo-product is strongly bipartite. Anothe...

In this paper, we introduce the notion of hyper pseudo B C K - algebras, which is a generalization of pseudo BCK -algebras and hyper BCK -algebras and we investigates some related properties. In follow, we de ne some kinds of hyper pseudo BCK -ideals of a hyper pseudo BCK - algebra and we find the relations among them. Finally, we characterize the hyper pseudo BCK -ideals of type 4 generated by...

Characterizations of fuzzy ideals of a pseudo-BCK algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. Given a fuzzy set μ, the least fuzzy ideal containing μ is constructed. The homomorphic properties of fuzzy ideals of a pseudo-BCK algebra are provided. Finally, characterizations of Noetherian pseudo-BCK algebras and Artinian pseudo-BCK algebras in terms of fuzzy...

The aim of this paper is to study the properties of dual BCK-algebra and to prove that the MV -algebra is equvalent to the bounded commutative dual BCK-algebra.

Imai and Iséki [1] introduced the concept of BCK-algebra as a generalization of notions of set difference operation and propositional calculus. The notion of pseudo-BCK algebra was introduced by Georgescu and Iorgulescu [2] as generalization of BCK-algebras not assuming commutativity. Hájek [3] introduced the concept of BL-algebras as the general semantics of basic fuzzy logic (BL-logic). Iorgu...

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...

A normal pseudo-BCK-algebra X is an algebra in which every subalgebra of X is an ideal of X . Characterizations of normal pseudo-BCK-algebras are given. 2010 Mathematics Subject Classification: 03G25, 06F35.

Characterizations of fuzzy ideals of a pseudo-BCK algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. Given a fuzzy set μ, the least fuzzy ideal containing μ is constructed. The homomorphic properties of fuzzy ideals of a pseudoBCK algebra are provided. Finally, characterizations of Noetherian pseudo-BCK algebras and Artinian pseudo-BCK algebras via fuzzy ideals a...

We prove that every implicative aBE algebra satisfies the transitivity property. This means is a Tarski algebra, and thus also commutative BCK algebra.