• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.207-214
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• 2019

The notions of a fuzzy simple BCK/BCI-algebra and an (${\in},{\in}{\vee}q$)-fuzzy simple BCK/BCI-algebra are introduced. Using these notions, characterizations of a simple BCK/BCI-algebra are considered.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.1-11
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• 2009

The notion of a BCK-algebra with supremum (briefly, sBCK-algebra) is introduced, and several examples are given. Related properties are investigated. We show that every sBCK-algebra with an additional condition has the condition (S). The notion of a dry ideal of an sBCK-algebra is introduced. Conditions for an sBCK-algerba to be an spBCK-algebra are provided. We show that every sBCK-algebra satisfying additional condition is a semi-Brouwerian algebra.

• 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.24 no.3
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• pp.333-339
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• 2009

In this manuscript, we introduce the concept of an atomic subset of the hyper BCK-algebra and study its properties. Also, we give a characterization of the atomic hyper BCK-algebra and show that there are exactly (up to isomorphism) n atomic hyper BCK-algebras H with |H| = n for any natural number n.

• 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.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 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.

• 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.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.51-62
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• 2002

The present paper gives a new construction of a quotient BCI(BCK)-algebra X/${\mu}$ by a fuzzy ideal ${\mu}$ in X and establishes the Fuzzy Homomorphism Fundamental Theorem. We show that if ${\mu}$ is a fuzzy ideal (closed fuzzy ideal) of X, then X/${\mu}$ is a commutative (resp. positive implicative, implicative) BCK(BCI)-algebra if and only if It is a fuzzy commutative (resp. positive implicative, implicative) ideal of X Moreover we prove that a fuzzy ideal of a BCI-algebra is closed if and only if it is a fuzzy subalgebra of X We show that if the period of every element in a BCI-algebra X is finite, then any fuzzy ideal of X is closed. Especiatly, in a well (resp. finite, associative, quasi-associative, simple) BCI-algebra, any fuzzy ideal must be closed.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.343-349
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• 1999

In this paper we apply the notion of $\rhd$$\mu$ and $\lhd$$\mu$ to fuzzy BCK-algebra, and show that $\lhd$$\mu$ is cogradient to a partial order of the BCK-algebra.