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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.

CHARACTERIZATIONS OF FUZZY FATED FILTERS OF $R_0$-ALGEBRAS BASED ON FUZZY POINTS