In this paper, bondage and non-bondage set of a fuzzy graph are discussed. The bondage number b(G) and non-bondage number b n (G) of a fuzzy graph G are defined. The upper bound for both b(G) and b n (G) are given. Also some results on b(G) and b n (G) are discussed. The exact values of b(G) and b n (G) are determined for several classes of fuzzy graphs.

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More general form of the notion of quasi-coincidence of a fuzzy point with a fuzzy subset is considered, and generalization of fuzzy fated of R0-algebras is discussed. The notion of an (∈, ∈ ∨ q k )-fuzzy fated filter in a R0-algebra is introduced, and several properties are investigated. Characterizations of an (∈, ∈ ∨ q k )-fuzzy fated filter in an R0-algebra are discussed. Using a collection of fated filters, a (∈, ∈ ∨ q k )-fuzzy fated filter is established.