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, ...

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.

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...

We investigate the rigidity of hyperbolic cone metrics on 3-manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyperideal hyperbolic polyhedral metrics. It is shown that a hyper-ideal hyperbolic polyhedral metric is determined up to isometry by its curvature and a decorated ideal hyperbolic polyhedral metric is d...

The notion of ∈-soft set and q-soft set based on a fuzzy set is introduced, and characterizations for an ∈-soft set and a q-soft set to be (idealistic) soft BCK/BCIalgebras are provided. Using the notion of (∈,∈∨ q)-fuzzy BCK/BCI subalgebras/ideals, characterizations for an ∈-soft set and a q-soft set to be (idealistic) soft BCK/BCI-algebras are established. AMS subject classifications: 06D72, ...

We introduce the notion of a Smarandache hyper (∩,∈)-ideal and Ω-reflexive in hyper K-algebra, and some related properties are given. Mathematics Subject Classification: 06F35, 03G25

In this paper the notion of fuzzy dot BCK-subalgebra is introduced. We state and prove some theorem in fuzzy dot BCK-subalgebra and level subalgebras. Mathematics Subject Classification: 06F35, 03G25, 94D05