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

First we show that the cosets of a fuzzy ideal μ in a BCK-algebraX form another BCK-algebra  X/μ (called the fuzzy quotient BCK-algebra of X by μ). Also we show thatX/μ is a fuzzy partition of X and we prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BCK-algebra iscompatible, then P is a fuzzy quotient BCK-algebra. Finally we define thenotion of a coset of a fuzzy ideal and an element of a BCK-algebra and proverelated theorems.

Keywords:

Fuzzy similarity relations , Fuzzy partitions , Fuzzy quotient , Fuzzy ideal , Cosets , Quotient algebra