Fuzziness of rough sets generated by a covering

Many theories and methods have been studied for the uncertainty measure of rough sets generated by a covering. This paper reviews all these methods and give some examples to illustrate their limitations. Then a novel uncertainty measure is developed based on the construction of a mapping from a covering based rough set to a fuzzy set through assigning a degree of rough belongingness to every object in the universe. The connection between rough sets and fuzzy sets is constructed and some important properties are derived. Analysis shows that this uncertainty measure overcomes the limitations of previous measures. The application of this measure in reduction of incomplete information systems is illustrated by an example in the end.