#### Paper Information

Journal:   IRANIAN JOURNAL OF FUZZY SYSTEMS   October 2004 , Volume 1 , Number 2; Page(s) 33 To 33.

Paper:

# SOME QUOTIENTS ON A BCK-ALGEBRA GENERATED BY A FUZZY SET

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Abstract:
In this paper at first we show that the cosets of a fuzzy ideal $\mu$ in a BCK–algebra $X$ form another BCK–algebra $frac{\mu}{X}$ called the fuzzy quotient BCK–algebra of X by $\mu$. Also we show that $frac{\mu}{X}$ is a fuzzy partition of $X$, and some isomorphism theorems are proved. Moreover we prove that, if the associated fuzzy similarity relation of a fuzzy partition $P$ of a commutative BCK–algebra is compatible, then $P$ is a fuzzy quotient BCK–algebra. Finally the notion of a coset of a fuzzy ideal and an element of a BCK-algebra is defined and some related theorems are proved.

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