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

• Journal of applied mathematics & informatics
• /
• v.26 no.3_4
• /
• pp.707-720
• /
• 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
• /
• v.9 no.2
• /
• pp.265-270
• /
• 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)

• Journal of the Chungcheong Mathematical Society
• /
• v.12 no.1
• /
• pp.15-21
• /
• 1999

In this paper, we introduce the notion of anti fuzzy prime ideals in a commutative BCK-algebra and obtain some properties of it.

• The Mathematical Education
• /
• v.19 no.2
• /
• pp.15-16
• /
• 1981

In this note, I studied about involution on BCK-algebras, and solved a problem posed by K. Iseki [4]. The problem is following: Is there a non-commutative BCK-algebra satisfying NN$\chi$=$\chi$\ulcorner.

• Honam Mathematical Journal
• /
• v.32 no.2
• /
• pp.217-226
• /
• 2010

Using the Bu$\c{s}$neag's model ([1, 2, 3]), the notion of pseudo-valuations (valuations) on a ${\mathbf{BCK/BCI}}$-algebra is introduced, and a pseudo-metric is induced by a pseudo-valuation on ${\mathbf{BCK/BCI}}$-algebras. Based on the notion of (pseudo) valuation, we show that the binary operation in ${\mathbf{BCK/BCI}}$-algebras is uniformly continuous.

• Communications of the Korean Mathematical Society
• /
• v.10 no.1
• /
• pp.11-14
• /
• 1995

In [1], Alo and Deeba introduced the uniformity of a BCK-algebra by using ideals. Meng [5] introduced the concept of dual ideals in BCK-algebras. We note that the concept of dual ideals is not a dual concept of ideals. In this paper, by using dual ideals, we consider the uniformity of a BCK-algebra.

• Communications of the Korean Mathematical Society
• /
• v.28 no.1
• /
• pp.11-24
• /
• 2013

The notion of intersectional soft sets is introduced, and several examples are given. The application of intersectional soft sets to BCK/BCI-algebras is discussed.

• Honam Mathematical Journal
• /
• v.30 no.1
• /
• pp.65-74
• /
• 2008

The notion of vague quick ideals of BCK/BCI-algebras is introduced, and several properties are investigated. Relations between a vague ideal, a vague BCK/BCI-algebra and a vague quick ideal are provided. A condition for a vague quick ideal to be a vague ideal is given.

• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.369-383
• /
• 2007

This paper is devoted to the foldness theory of implicative ideals in BCK-algebras. We use the fuzzy point concept to give some characterizations of fuzzy n-fold implicative ideals and establish some relationships with various n-fold ideals. We also construct some algorithms for studying the foldness of implicative ideals in BCK-algebras.