• 제목/요약/키워드: fuzzy quotient BCK-algebra

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

  • Liu, Yong-Lin;Jie Meng
    • Journal of applied mathematics & informatics
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    • 제10권1_2호
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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.

FUZZY QUOTIENT STRUCTURES OF BCK-ALGEBRAS INDUCED BY FUZZY BCK-FILTERS

  • Jun, Young-Bae
    • 대한수학회논문집
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    • 제21권1호
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    • pp.27-36
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    • 2006
  • In this paper, we establish a generalization of fundamental homomorphism theorem in BCK-algebras by using fuzzy BCK-filters. We prove that if ${\mu}$. (resp. v) is a fuzzy BCK-filter of abounded BCK-algebra X (resp. Y), then $\frac{X{\times}Y}{{\mu}{\times}v}{\approxeq}X/{\mu}{\times}Y/v;\;and\;if\;{\mu}$ and F is a BCK-filter in a bounded BCK-algebra X such that $F/{\mu}$ is a BCK-filter of $X/{\mu}$, then $\frac{X/{\mu}}{F/{\mu}}{\approxeq}X/F$.