• 충청수학회지
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• 제32권2호
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• pp.207-214
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• 2019

The notions of a fuzzy simple BCK/BCI-algebra and an (${\in},{\in}{\vee}q$)-fuzzy simple BCK/BCI-algebra are introduced. Using these notions, characterizations of a simple BCK/BCI-algebra are considered.

• 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.