• 대한수학회보
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• 제36권2호
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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.

• 호남수학학술지
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• 제34권2호
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• pp.145-159
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• 2012

Several types of a bipolar fuzzy hyper BCK-ideal in a hyper BCK-algebra are introduced, and their relations are investigated.

• 대한수학회논문집
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• 제8권2호
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• pp.225-231
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• 1993

• East Asian mathematical journal
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• 제21권1호
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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].

• East Asian mathematical journal
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• 제21권1호
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• pp.9-19
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• 2005

In this paper, some properties of intuitionistic fuzzy o-subalgebras of BCK-algebra with condition(S) are investigated.

• 충청수학회지
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• 제20권3호
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• pp.279-286
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• 2007

Using t-norm T and s-norm S, we introduce the notion of intuitionistic (T, S)-normed fuzzy subalgebra in BCK/BCI-algebra, and some related properties are investigated.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.243-250
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• 2003

The fuzzification of (Positive implicative) pseudo-ideals in a pseudo-BCK algebra is discussed, and several properties are investigated. Characterizations of a fuzzy pseudo-ideal are displayed.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권1호
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• pp.73-84
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• 2008

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Aranassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to commutative ideals in BCK-algebras. The notion of an intuitionistic fuzzy commutative ideal of a BCK-algebra is introduced, and some related properties are investigated. Characterizations of an intuitionistic fuzzy commutative ideal are given. Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy commutative ideal are given. Using a collection of commutative ideals, intuitionistic fuzzy commutative ideals are established.

• 대한수학회논문집
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• 제20권2호
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• pp.221-229
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• 2005

In this paper we consider the decompositions of subdirect sums and direct sums in bounded BCK-algebras. The main results are as follows. Given a bounded BCK-algebra X, if X can be decomposed as the subdirect sum $\bar{\bigoplus}_{i{\in}I}A_i$ of a nonzero ideal family $\{A_i\;{\mid}\;i{\in}I\}$ of X, then I is finite, every $A_i$ is bounded, and X is embeddable in the direct sum $\bar{\bigoplus}_{i{\in}I}A_i$ ; if X is with condition (S), then it can be decomposed as the subdirect sum $\bar{\bigoplus}_{i{\in}I}A_i$ if and only if it can be decomposed as the direct sum $\bar{\bigoplus}_{i{\in}I}A_i$ ; if X can be decomposed as the direct sum $\bar{\bigoplus}_{i{\in}I}A_i$, then it is isomorphic to the direct product $\prod_{i{\in}I}A_i$.

• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.433-436
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• 2006

In this note we show that a representable difference algebra is equivalent to a commutative BCK-algebra.