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Zbl 0935.06019
Meng, J.; Xin, X.L.; Pu, Y.S.
Quotient BCK-algebra induced by a fuzzy ideal. (English)
[J] Southeast Asian Bull. Math. 23, No.2, 243-251 (1999). ISSN 0129-2021; ISSN 0219-175X/e

Continuing previous work of the first author, {\it Y. B. Yun} and {\it H. S. Kim} [Fuzzy Sets Syst. 89, No. 2, 243-248 (1997; Zbl 0914.06009)], the authors show that a non-constant fuzzy ideal $\mu$ of a BCK-algebra $X$ allows to build up the quotient BCK-algebra $X/\mu$, which is implicative, positive implicative and commutative if $\mu$ has, suitably ``fuzzified'', the respective properties. Among others, the authors prove the so-called ``Fuzzy Homomorphism Fundamental Theorem'': Let $f$ be a homomorphism of $X$ onto the BCK-algebra $Y$. Let $\nu$ be a fuzzy ideal of $Y$ and $\mu = \nu \circ f$ the preimage of $\nu$ under $f$. Then $X/\mu$ and $Y/ \nu$ are isomorphic.
[S.Sessa (Napoli)]

MSC 2000:: *06F35 BCK-algebras, etc.

Keywords: BCK-algebra; fuzzy ideal; quotient

Citations: Zbl 0914.06009

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