A Many-Valued Approach to Fuzzy Rough Set

In this paper, in the framework of many-valued logic, the crisp lower and upper approximation operators of rough set theory are generalized to fuzzy environment, and the basic properties of that two operators are studied. Also, it is proved that our upper approximation operator is a generalization of
T
-upper fuzzy approximation operator defined by Mi [cf. J.S. Mi, Y. Leung, H.Y. Zhao, T. Feng, Generalized fuzzy rough sets determined by a triangular norm, Information Sciences 178(2008) 3203-3213], but the lower approximation is quite different from the corresponding
T
-lower fuzzy approximation operator.