On fuzzy quotient BCK-algebras

Abstract

In this paper, by considering the concept of fuzzy congruence in some algebraic structures, we specially study fuzzy congruence in BCK-algebras. We prove that there is a bijection between the set of fuzzy ideals and the set of fuzzy congruences in BCK-algebras. Then we show that for each fuzzy ideal µ, there is an associated algebra X/µ that is a BCK-algebra. Also, we obtain a congruence relation on a BCK-algebra by fuzzy ideals.