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FUZZY SUB-IMPLICATIVE IDEALS OF BCI-ALGEBRAS

  • Jun, Young-Bae
    • Bulletin of the Korean Mathematical Society
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    • v.39 no.2
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    • pp.185-198
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    • 2002
  • We Consider the fuzzification of sub-implicative ideals in BCI-algebras, and investigate some related properties. We give conditions for a fuzzy ideal to be a fuzzy sub-implicative ideal. we show that (1) every fuzzy sub-implicative ideal is a fuzzy ideal, but the converse is not true, (2) every fuzzy sub-implicative ideal is a fuzzy positive implicative ideal, but the converse is not true, and (3) every fuzzy p-ideal is a fuzzy sub-implicative ideal, but the converse is not true. Using a family of sub-implicative ideals of a BCI-algebra, we establish a fuzzy sub-implicative ideal, and using a level set of a fuzzy set in a BCI-algebra, we give a characterization of a fuzzy sub-implicative ideal.

Fuzzy Positive Implicative Hyper K-ideals in Hyper K-algebras

  • Jun, Young Bae;Shim, Wook Hwan
    • Honam Mathematical Journal
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    • v.25 no.1
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    • pp.43-52
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    • 2003
  • The fuzzification of positive implicative hyper K-ideals in hyper K-algebras is considered, Relations between fuzzy positive implicative hyper K-ideal and fuzzy hyper K-ideal are given. Characterizations of fuzzy positive implicative hyper K-ideals are provided. Using a family of positive implicative hyper K-ideals we make a fuzzy positive implicative hyper K-ideal. Using the notion of a fuzzy positive implicative hyper K-ideal, a weak hyper K-ideal is established.

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POSITIVE IMPLICATIVE MBJ-NEUTROSOPHIC IDEALS IN BCK-ALGEBRAS

  • Roh, Eun Hwan
    • Honam Mathematical Journal
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    • v.44 no.2
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    • pp.209-218
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    • 2022
  • The notion of positive implicative MBJ-neutosophic ideal of BCK-algebras is defined and some properties of it are investigated. Relations between positive implicative MBJ-neutrosophic ideal and positive implicative ideal are discussed. In a BCK-algebra, the extension property for positive implicative MBJ-neutrosophic ideal is established.

CONSTRUCTION OF QUOTIENT BCI(BCK)-ALGEBRA VIA A FUZZY IDEAL

  • Liu, Yong-Lin;Jie Meng
    • 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.

INTUITIONISTIC FUZZINESS OF IMPLICATIVE IDEALS IN BCK-ALGEBRAS

  • Jun, Young-Bae;Park, Chul-Hwan;Roh, Eun-Hwan
    • Honam Mathematical Journal
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    • v.29 no.3
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    • pp.377-402
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    • 2007
  • 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 implicative ideals in BCK-algebras. The notion of an intuitionistic fuzzy implicative ideal of a BCK-algebra is introduced, and some related properties are investigated. An extension property for intuitionistic fuzzy implicative ideals is established. Characterizations of an intuitionistic fuzzy implicative ideal are given. Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy implicative ideal are given. Using a collection of implicative ideals, intuitionistic fuzzy implicative ideals are established.

Weak positive implicative hyperBCK-ideal

  • Kim, Y.H.;Namkoong, Y.M.;T.E. Jeong
    • 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.

FUZZY SET THEORY APPLIED TO IMPLICATIVE IDEALS IN BCK-ALGEBRAS

  • Jun, Young-Bae;Song, Seok-Zun
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.3
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    • pp.461-470
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    • 2006
  • As a continuation of [4], characterizations of fuzzy implicative ideals are given. An extension property for fuzzy implicative ideals is established. We prove that the family of fuzzy implicative ideals is a completely distributive lattice. Using level subsets of a BCk-algebra X with respect to a fuzzy set $\={A}$ in X, we construct a fuzzy implicative ideal of X containing $\={A}$.