In this paper, we introduce the notions of an interval-valued intuitionistic fuzzy positive implicative hyper BCK-ideal of types-1,2,3,…,8. Then we present some theorems which characterize the above notions according to the intervalvalued level subsets. Also we obtain certain relationships among these notions, interval-valued intuitionistic fuzzy (strong, weak) hyper BCK-ideals and interval-valued intuitionistic fuzzy positive implicative hyper BCK-ideals of types-1,2,3,..,8 and obtain some related results.
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