The aim of this paper is to apply the concept of interval-valued intuitionistic fuzzy set to implicative ideals and commutative ideals in BCK-algebras and introduced the new notion of interval-valued intuitionistic fuzzy implicative ideals in BCK-algebras and interval-valued intuitionistic fuzzy commutative ideals in BCK-algebras and related properties are investigated.

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, ...

In this paper, we investigate the ideal theory in BCK-algebras and we define the notions of primary and P -primary ideals. Then we show that in bounded implicative BCK-algebras, if an ideal has a primary decomposition, then it has a reduced primary decomposition. In the follow, we extend the above concepts to X-modules (Extended BCK-modules) and we introduce the notions of primary and P -primar...

Molodtsov [5] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to an implicative ideal of BCK-algebras. The notion of implicative soft ideals in BCKalgebras and implicative idealistic soft BCK-algebras is ...

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...

The aim of this paper is to derive pseudo-BCK algebras from directoids and vice versa. We generalize some results proved by Ivan Chajda et al. in the case BCK-algebras. assign an arbitrary algebra a semilattice-like structure observe that point where are different structures. Finally, relation between commutative deductive systems bounded pseudo-BCK(pDN) characterization terms discussed.

The intuitionistic fuzzification of (strong, weak, s-weak) hyperBCK-ideals is introduced, and related properties are investigated. Characterizationsof an intuitionistic fuzzy hyper BCK-ideal are established. Using acollection of hyper BCK-ideals with some conditions, an intuitionistic fuzzyhyper BCK-ideal is built.

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...

In this paper, by considering the notion of ∧-closed set in BCK-algebras, we construct the fractions of BCK-algebras and we get some related results.

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...