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Rough set theory is a powerful tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. In this paper we study covering-based rough fuzzy sets in which a fuzzy set can be approximated by the intersection of some elements in a covering of the universe of discourse. Some properties of the covering-based fuzzy lower and upper approximation operators are examined. We present the conditions under which two coverings generate the same coveringbased fuzzy lower and upper approximation. We approximate fuzzy sets based on a binary relation and its properties are introduced. Finally, we establish the equivalency between rough fuzzy sets generated by a covering and rough fuzzy sets generated by a binary relation. , FH(b) = 1 2 , FH(c) = 2 3 , FH(d) = 2 3 . On the other hand, SL(a) = 1 3 , SL(b) = 0, SL(c) = 0, SL(d) = 2 3 and SH(a) = 1 3 , SH(b) = 1 2 , SH(c) = 1 2 , SH(d) = 2 3 . Therefore, FL(X) ⊆ SL(X) and SH(X) ⊆ FH(X).