Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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CONSTRUCTION OF QUOTIENT BCI(BCK)-ALGEBRA VIA A FUZZY IDEAL

  • Liu, Yong-Lin (Department of Mathematics, Nanping Teachers College) ;
  • Jie Meng (Department of Mathematics, Northwest University)
  • Published : 2002.09.01

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Abstract

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.

Keywords

References

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