Copyright q 2010 Young Bae Jun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Based on the theory of falling shadows and fuzzy sets, the notion of a falling fuzzy implicative ideal of a BCK-algebra is introduced. Relations...

In 1982, Pawlak introduced the concept of a rough set (see [6]). This concept is fundamental for the examination of granularity in knowledge. It is a concept which has many applications in data analysis (see [7]). Rough set theory is applied to semigroups and groups (see [4, 5]), and BCK-algebras (see [3]). In this paper, we apply the rough set theory to BCC-algebras, and we discuss the notion ...

Given Φ,Ψ ∈ {∈, q,∈ ∨ q}, the notion of (Φ, Ψ)neutrosophic subalgebras of a BCK/BCI-algebra are introduced, and related properties are investigated. Characterizations of an (∈,∈)neutrosophic subalgebra and an (∈,∈∨ q)-neutrosophic subalgebra are provided. Given special sets, so called neutrosophic ∈-subsets, neutrosophic q-subsets and neutrosophic ∈∨ q-subsets, conditions for the neutrosophic ∈...

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, by considering the notion of hyper hoop-algebras, we define the concepts of (strong) regular relations on hyper hoop-algebras and investigate some properties of them. Then we construct a quotient (hyper) hoop-algebra by a (strong)regular relation on hyper hoop-algebras. Finally, we define the notion of maximal filter and we investigate the relation between quotient simple hyper h...

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 ...

This paper provides a review on major ergodic features of semiindependent hyper MV –algebra dynamical systems. Theorems are presented to make contribution to calculate the entropy. Particularly, it is proved that the total entropy of those semi-independent hyper MV –algebra dynamical systems that have a generator can be calculated with respect to their generator rather than considering all the ...

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.

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, ...

Neutrosophic set has the ability to handle uncertain, incomplete, inconsistent, indeterminate information in a more accurate way. In this paper, we proposed a neutrosophic recommender system to predict the diseases based on neutrosophic set which includes single-criterion neutrosophic recommender system (SCNRS) and multi-criterion neutrosophic recommender system (MC-NRS). Further, we investigat...