Abstract
The present paper gives a new construction of a quotient BCI(BCK)- algebra X/µ by a fuzzy ideal µ in X and establishes the Fuzzy Homomorphism Fundamental Theorem. We show that if µ is a fuzzy ideal (closed fuzzy ideal) of X. then X/µ is a commutative (resp. positive implicative, implicative) BCK(BCI)- algebra if and only if µ 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. Especially, in a well (resp. finite, associative, quasi-associative, simple) BCI-algebra, any fuzzy ideal must be closed.
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