• Journal for History of Mathematics
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• v.20 no.1
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• pp.73-82
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• 2007

This paper delineates some history and developments of Wajsberg hoops, MV-algebras and commutative BCK-algebras. It also discuss some relations on them. Finally, it shows that every Wajsberg hoop is a commutative BCK-algebra.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.707-720
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• 2008

Molodtsov [12] 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 commutative ideals of BCK-algebras, The notions of commutative soft ideals and commutative idealistic soft BCK-algebras are introduced, and their basic properties are investigated. Examples to show that there is no relations between positive implicative idealistic soft BCK-algebras and commutative idealistic soft BCK-algebras are provided.

• 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.46 no.1
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• pp.147-153
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• 2009

In this paper, we give some constructions of implicative/commutative d-algebras which are not BCK-algebras. This demonstrate that the notion of implicative/commutative d-algebras are indeed generalizations of the same in BCK-algebras.

• The Pure and Applied Mathematics
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• v.15 no.1
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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.

• 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.

• 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.

• 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 $BCK^{\star}(X)$.

• Kyungpook Mathematical Journal
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• v.46 no.3
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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.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.17-27
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• 2013

The notions of the extensions of bipolar fuzzy ideals, bipolar fuzzy prime ideals and bipolar fuzzy commutative ideals in BCK-algebras are introduced, and several properties are investigated.