Abstract: In this note first we define the notions of intuitionistic
fuzzy dual positive implicative hyper K-ideals of types
1,2,3,4 and intuitionistic fuzzy dual hyper K-ideals. Then we
give some classifications about these notions according to the
level subsets. Also by given some examples we show that these
notions are not equivalent, however we prove some theorems
which show that there are some relationships between these
notions. Finally we define the notions of product and antiproduct
of two fuzzy subsets and then give some theorems
about the relationships between the intuitionistic fuzzy dual
positive implicative hyper K-ideal of types 1,2,3,4 and their
(anti-)products, in particular we give a main decomposition
theorem.