Abstract
The objective of this paper is to provide a new generalizations of rough fuzzy sets in generalized approximation space. The equivalance relations are viewed as a special type of an binary relations of a universe. Then, the rough fuzzy sets in generalized approximation space is defined. Furthermore, the relationships between generalizations rough fuzzy sets and the rough fuzzy sets, which is proposed by Dubois and Prade first time, Pawlak rough set , etc are investigated. Some propseties of the generalizations rough fuzzy sets are discussed. Meanwhile, the roughness and precision of the generalizations rough fuzzy sets are illuminated, too. At last, the definitions of the rough fuzzy sets in generalized approximation space based on the others binary relations are built.
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