Generalized Fuzzy Ideals of BCK-Algebras

Abstract

In this paper, the concepts of generalized fuzzy sub-algebras , generalized fuzzy ideals and generalized fuzzy implicative ideals of BCK-algebras are introduced. The following results are obtained: for a BCK-algebra X, any generalized fuzzy ideal of X must be a generalized fuzzy sub-algebra; a fuzzy set A of X is a generalized fuzzy ideal (implicative ideal) of X if and only if, for all t ¿ (¿, ¿), A _t is either empty or an ideal (implicative ideal) of X; suppose that A and B are generalized fuzzy ideals of X with A ¿ B b, if A is a generalized fuzzy implicative ideal of X, then so is B. Also, several characterizations of generalized fuzzy implicative ideals are given.