Fuzzy multiply positive implicative hyper BCK-ideals of hyper BCK-algebras

We consider the fuzzification of the notion of fuzzy multiply positive implicative hyper BCK-ideals of BCK-algebras and then some related results are obtained. Using the concept of level subsets, we give a characterization of a fuzzy multiply positive implicative hyper BCK-ideal. We state a relation between a fuzzy hyper BCK-ideal and a fuzzymultiply positive implicative hyper BCK-ideal. Moreover, we introduce the notions of Noetherian hyper BCKalgebras and hyper homomorphisms of hyper BCK-algebras and investigate some related properties. Finally, we introduce the concept of hyper normalization of hyper BCK-algebras and discuss related properties.