• 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.

• 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.

• 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.

• 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.

• East Asian mathematical journal
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• v.17 no.1
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• pp.115-128
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• 2001

We present old unsolved problems on BCK-sequences connected with convex congruences on BCK-algebras. We posed also some new problems on subalgebras.

• 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.

• 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.9 no.2
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• pp.265-270
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• 1994

In 1966, Iseki [2] introduced the notion of BCI-algebras which is a generalization of BCK-algebras. Lei and Xi [3] discussed a new class of BCI-algebra, which is called a p-semisimple BCI-algebra. For p-semisimple BCI-algebras, a subalgebra is an ideal. But a subalgebra of an arbitrary BCI/BCK-algebra is not necessarily an ideal. In this note, a BCI/BCK-algebra that every subalgebra is an ideal is called a normal BCI/BCK-algebra, and we give characterizations of normal BCI/BCK-algebras. Moreover we give a positive answer to the problem which is posed in [4].(omitted)

• 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 the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.131-139
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• 2009

As a generalization of a homomorphism of BCK-algebras, the notion of a semi-homomorphism of BCK-algebras is introduced, and its characterization is given. A condition for a semi-homomorphism to be a homomorphism is provided.