• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.11-15
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• 1996

In this paper we prove that if Y is a poset of the form $\underline{1}{\oplus}Y^{\prime}$ for some subposet Y' then BCK(Y) is a ${\Gamma}$-BCK-algebra. Moreover, if X is a BCI-algebra then Hom(X, BCK(Y)) is a positive implicative ${\Gamma}$-BCK-algebra.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.261-262
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• 2016

We present a short and very elementary proof that each finite BCK-algebra is solvable. It is a positive answer to the question posed in [4].

• East Asian mathematical journal
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• v.26 no.3
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• pp.379-387
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• 2010

In this paper, we prove that the extension ideal of a fuzzy characteristic ideal of a positive implicative BCK-algebra is a fuzzy characteristic ideal. We introduce the notion of the extension of intuitionistic fuzzy ideal of BCK-algebras and some properties of fuzzy intuitionistic ideal extensions of BCK-algebra are investigated.

• East Asian mathematical journal
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• v.21 no.1
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• pp.49-60
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• 2005

In this paper we introduced Semi-neutral BCK-algebra and investigate some of its properties. The notions of ideals and subalgebras coincide in Semi-neutral BCK-algebras. We also show that if the number of nonzero elements in a Semi-neutral BCK-algebra is n, then the number of ideals/subalgebras in it is $2^n$. Further, we solved an open problem posed by W.A. Dudek in [2].

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.2
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• pp.243-246
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• 2003

In this paper we define a weak positive implicative hyperBCK-ideal of hyperBCK-algebra. Also we investigate that every positive implicative hyperBCK-algebra is a positive implicative hyperK-algebra and then we prove that every positive implicative hyperK-algebra is a weak positive implicative hyperk-algebra.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.183-196
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• 2011

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 BCK-algebras and implicative idealistic soft BCK-algebras is introduced, and related properties are investigated. Relations between implicative soft ideals and commutative (resp. positive implicative) soft ideals are discussed. Also, relations between implicative idealistic soft BCK-algebras and commutative (resp. positive implicative) idealistic soft BCK-algebras are provided.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.53-58
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• 1998

In this paper we study (positive) implicativeness of $BCK^{\star}(X^{\star})$, and investigate some properties of ideals in $BCK^{\star}(X)$.

• Journal of the Korean Institute of Intelligent Systems
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• v.6 no.3
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• pp.89-93
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• 1996

In this paper, we investigated the relation between the ideals of BCK-algebras and fuzzy ideals. We defined the weakly implicative ideals of BCK-algebras and obtained some properties. We proved some results for the fuzzy weakly implicative ideals of bounded commutative BCK-algebras. We also investigated that the weakly implicative ideals are similar to the fuzzy positive implicative ideals.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.367-379
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• 2011

Fuzzy ${\alpha}$-translations, (normalized, maximal) fuzzy extensions and fuzzy multiplications of fuzzy hyper BCK-subalgebras in hyper BCK-algebras are discussed. Relations among fuzzy ${\alpha}$ translations, (normalized, maximal) fuzzy extensions and fuzzy multiplications are investigated.