• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.385-403
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• 2011

Generalizations of the notion of fuzzy hyper K-subalgebras are considered. The concept of fuzzy hyper K-subalgebras of type (${\alpha},{\beta}$) where ${\alpha}$, ${\beta}$ ${\in}$ {${\in}$, q, ${\in}{\vee}q$, ${\in}{\wedge}q$} and ${\alpha}{\neq}{\in}{\wedge}q$. 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.