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, ...

It is evident from the definition that the class of all BCK-algebras is a quasivariety. Yet it is not a variety, nor does the largest subvariety of BCK exist—as shown in Wroński [2], Kabziński & Wroński [3], respectively. Several subvarieties of BCK have been isolated and thoroughly investigated, which has led to a substantial body of results (cf. e.g., Blok & Raftery [4]). Nevertheless, the qu...

The foldness of PI( , ⊆, ⊆)BCK -ideals and PI( , , )BCK -ideals is considered. The fuzzy version of such notions is also discussed.

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 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...

in this paper, we aresupposed to introduce the definitions of n-fold commutative, andimplicative hyper k-ideals. these definitions are thegeneralizations of the definitions of commutative, andimplicative hyper k-ideals, respectively, which have been definedin [12]. then we obtain some related results. in particular wedetermine the relationships between n-fold implicative hyperk-ideal and n-fold...

Neutrosophic N -structures with applications in BCK/BCI-algebras is discussed. The notions of a neutrosophic N -subalgebra and a (closed) neutrosophic N -ideal in a BCK/BCI-algebra are introduced, and several related properties are investigated. Characterizations of a neutrosophic N -subalgebra and a neutrosophic N -ideal are considered, and relations between a neutrosophic N -subalgebra and a ...

In this paper, first we introduce the notions of k-nilpotent (solvable) ideals and BCK-algebras. Specially, show that every commutative ideal is 1-nilpotent (solvable). Second, state an equivalent condition to k-nilpotency (solvablity) BCK-algebra. Finally, study n-fold 2-nilpotent BCK-algebras as a generalization BCK-algebras, relation between these two concepts. Basically, compare solvable (B...

In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the not...