  The most general form of the notion of quasi-coincidence of a fuzzy point
with a fuzzy subset is considered, and generalization of fuzzy fated of
$R_0$-algebras is discussed. The notion of an $(\epsilon , \epsilon \vee
q_k)$-fuzzy fated filter in an $R_0$-algebra is introduced, and several
properties are investigated. Characterizations of an $(\epsilon ,\epsilon \vee
q_k)$-fuzzy fated filter in an $R_0$-algebra are discussed. Using a collection
of fated filters, a $(\epsilon ,\epsilon \vee q_k)$-fuzzy fated filter is
established.
