This paper is devoted to the foldness theory of implicative ideals in BCK-algebras. We use the fuzzy point concept to give some characterizations of fuzzy n-fold implicative ideals and establish some relationships with various n-fold ideals. We also construct some algorithms for studying the foldness of implicative ideals in BCK-algebras. AMS Mathematics Subject Classification: 06F35, 13A15, 8A...

In this paper, we present the notions of cubic (weak) implicative hyper BCK-ideals of hyper BCKalgebras and then we present some results which characterize the above notions according to the level subsets. In addition, we obtain the relationship among these notions, cubic positive implicative hyper BCK-ideals of types-1, 2...8 and obtain some related results.AMS (2010): 06F35.

In the present manuscript, we introduce concept of a discrete dynamical system (Ⱬ,Ψ) in BCK-algebra where Ⱬ is and Ψ homomorphism from to establish some their related properties. We prove that set all fixed points periodic are BCK-subalgebras. show when subset invariant concerning Ψ. commutative with relative cancellation property ideals Ⱬ. also an S-invariant

In this paper, we introduce the notions of Belluce lattice associated with a bounded $BCK$-algebra and reticulation $BCK$-algebra. To do this, first, define operations $curlywedge ,$ $curlyvee $ $sqcup on $BCK$-algebras study some algebraic properties them. Also, for $A$ Zariski topology Spec(A)$ induced $tau _{A,Max(A)}$ $Max(A)$. We prove $(Max(A),tau_{A,Max(A)})$ is compact topological space...

Cantor's naive set theory is characterized by the unrestricted comprehension principle, saying that for every formula A(x), there exists a set {x|A(x)} such that A(t) ↔ t ∈ {x|A(x)} for any term t. The theory is intuitive, elegant, powerful, but unfortunately inconsistent (as witnessed by Russell's paradox). While it is common to somehow restrict the comprehension scheme (as in ZFC), there is a...

A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equiva...

This paper deals with the study of generalizations fuzzy subalgebras and ideals in BCK/BCI-algebras. In fact, notions ∈ , ∨ κ ~ ∗ q -fuz...

We consider the intuitionistic fuzzification of the concept of subalgebras and ideals in BCK-algebras, and investigate some of their properties. We introduce the notion of equivalence relations on the family of all intuitionistic fuzzy ideals of a BCK-algebra and investigate some related properties.

The concept of soft translations of soft subalgebras and soft ideals over BCI/BCK-algebras is introduced and some related properties are studied. Notions of Soft extensions of soft subalgebras and soft ideals over BCI/BCK-algebras are also initiated. Relationships between soft translations and soft extensions are explored.