• Honam Mathematical Journal
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• v.31 no.2
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• pp.157-166
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• 2009

Using more general form of the notion of quasi-coincidence of a fuzzy point with a fuzzy subset, the notion of ($({\in},{\in}{\bigvee}q_{\kappa})$)-fuzzy BCK-filters is introduced, and related properties are investigated. Many characterizations of ($({\in},{\in}{\bigvee}q_{\kappa})$)-fuzzy BCK-filters are provided. Relations between an ($({\in},{\in}{\bigvee}q_{\kappa})$)-fuzzy BCK-filter and a fuzzy BCK-filter are established.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.369-383
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• 2007

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.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.315-324
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• 2011

In this paper, we study the effects of a deformation mapping on the resulting deformation d/BCK-algebra obtained via such a deformation mapping. Besides providing a method of constructing d-algebras from BCK-algebras, it also highlights the special properties of the standard BCK-algebras of posets as opposed to the properties of the class of divisible d/BCK-algebras which appear to be of interest and which form a new class of d/BCK-algebras insofar as its not having been identified before.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.361-366
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• 2009

In this paper we consider constructive function triples on the real numbers $\mathbb{R}$ and on (not necessarily commutative) integral domains D which permit the construction of a multitude of d-algebras via these constructive function triples. At the same time these constructions permit one to consider various conditions on these d-algebras for subsets of solutions of various equations, thereby producing geometric problems and interesting visualizations of some of these subsets of solutions. In particular, one may consider what notions such as "locally BCK" ought to mean, certainly in the setting provided below.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.431-439
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• 2012

Characterizations of $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) are provided. The notion of $\mathcal{N}$-subalgebras of type ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) is introduced, and its characterizations are discussed. Conditions for an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) (resp. ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) to be an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}$) are considered.