In this manuscript we define the notions of positive implicative

hyper$K$-ideals of types 1,2,3 and 4. Then by given many examples

we show that these notions are different. After that we state and

prove some theorems which determine the relation between these

notions. Also by defining the concept of scalar element and

additive condition we obtain another results. Finally we give a

theorem which states that where the image and the inverse image of

a positive implicative hyper$K$-ideals are also positive

implicative hyper$K$-ideals under a homomorphism of

hyper$K$-algebras.