Generalizations of the notion of fuzzy hyper K-subalgebras are considered. The concept of fuzzy hyper K-subalgebras of type (${alpha},{eta}$) where ${alpha}$, ${eta}$ ${in}$ {${in}$, q, ${in}{vee}q$, ${in}{wedge}q$} and ${alpha}{ eq}{in}{wedge}q$. Relations between each types are investigated, and many related properties are discussed. In particular, the notion of (${in}$, ${in}{vee}q$)-fuzzy hyper K-subalgebras is dealt with, and characterizations of (${in}$, ${in}{vee}q$)-fuzzy hyper K-subalgebras are established. Conditions for an (${in}$, ${in}{vee}q$)-fuzzy hyper K-subalgebra to be an (${in}$, ${in}$)-fuzzy hyper K-subalgebra are provided. An (${in}$, ${in}{vee}q$)-fuzzy hyper K-subalgebra by using a collection of hyper K-subalgebras is established. Finally the implication-based fuzzy hyper K-subalgebras are discussed.