We consider the fuzzification of the notion of implicative hyper BCK-ideals, and then investigate several properties. Using the concept of level subsets, we give a characterization of a fuzzy implicative hyper BCK-ideal. We state a relation between a fuzzy hyper BCK-ideal and a fuzzy implicative hyper BCK-ideal. We establish a condition for a fuzzy hyper BCK-ideal to be a fuzzy implicative hyper BCK-ideal. Finally, we introduce the notion of hyper homomorphisms of hyper BCK-algebras, and discuss related properties. 2000 Mathematics Subject Classification: 06F35, 03G25, 20N20, 03B52. 1. Introduction. The hyper structure theory (called also multialgebras) is introduced in 1934 by Marty [5] at the 8th Congress of Scandinavian Mathematicians. Around the 40’s, several authors worked on hypergroups, especially in France and in the United States, but also in Italy, Russia, and Japan. Over the following decades, many important results appeared, but above all since the 70’s onwards the most luxuriant flourishing of hyper structures has been seen. Hyper structures have many applications to several sectors of both pure and applied sciences. Jun et al. [4] applied the hyper structures to BCK-algebras, and introduced the concept of a hyper BCK-algebra which is a generalization of a BCK-algebra, and investigated some related properties. They also introduced the notion of a hyper BCK-ideal and a weak hyper BCK-ideal, and gave relations between hyper BCK-ideals and weak hyper BCK-ideals. Jun and Xin [1] considered the fuzzification of the notion of a (weak, strong, reflexive) hyper BCK-ideal, and investigated the relations among them. In this paper, we deal with the fuzzification of the notion of implicative hyper BCK-ideals. We show that every fuzzy implicative hyper BCK-ideal is a fuzzy hyper BCK-ideal, but not converse. We provide a condition for a fuzzy hyper BCK-ideal to be a fuzzy implicative hyper BCK-ideal. Using the notion of level subsets of a fuzzy set, we give a characterization of a fuzzy implicative hyper BCK-ideal. We introduce the concept of hyper homomorphisms of hyper BCK-algebras, and we show that the hyper homomorphic preimage of a fuzzy implicative hyper BCK-ideal is also a fuzzy implicative hyper BCK-ideal.