In this note first we define the notions of {\it positive implicative hyper $BCK$-ideals of types 1,2,...,8}. Then, giving some examples, we show that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (strong, weak) hyper $BCK$-ideals. Finally will be presented, a classification of hyper $BCK$-algebras of order 3.