Georgescu and Iorgulescu [3] introduced pseudo-BCK-algebras (in a slightly different way) as a non-commutative generalization of BCK-algebras, in the sense that if →= , then the algebra (A,→, 1) is a BCK-algebra. Pseudo-BCK-algebras relate to (non-commutative) residuated lattices as BCK-algebras do to commutative residuated lattices; specifically, by [6], pseudoBCK-algebras are just the 〈→, , 1...

In this paper, we acquaint new kinds of ideals BCK-algebras built on tripolar picture fuzzy structures. fact, the notions ideal, implicative ideal (commutative ideal) BCK-algebra are introduced, and related properties studied. Also, a relation among is well-known. Furthermore, it shown that may be but converse not correct in common. Further, obtained an BCK-algebra, aforementioned statement tru...

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.

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...

In this paper, by considering the notion of extended BCK-module, we define the concepts of free extended BCK-module, free object in category of extended BCK-modules and we state and prove some related results. Specially, we define the notion of idempotent extended BCK-module and we get some important results in free extended BCK-modules. In particular, in category of idempotent extended BCK-mod...

Abstract In this paper, Sheffer stroke BCK-algebra is defined and its features are investigated. It indicated that the axioms of a independent. The relationship between stated. After describing commutative, an implicative involutory BCK-algebras, some important properties proved. structures demonstrated. A with condition (S) described connection other shown. Finally, it proved for to be Boolean...

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...

Pseudo-BCK algebras were introduced by G. Georgescu and A. Iorgulescu as a generalization of BCK algebras in order to give a corresponding structure to pseudo-MV algebras, since the bounded commutative BCK algebras corresponde to MV algebras. Properties of pseudo-BCK algebras and their connections with other fuzzy structures were established by A. Iorgulescu and J. Kühr. The aim of this paper i...

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.