Fuzziness in Covering Generalized Rough Sets

Rough sets theory has been considered as a useful method to model the uncertainty and has been applied successfully in many fields. And every rough set is associated with some amount of fuzziness. On the other hand, rough sets theory has been generalized with coverings instead of classical partition. So it is necessary to consider the amount of fuzziness in generalized rough sets induced by a covering. In this paper, a measure of fuzziness in generalized rough sets induced by a covering is proposed. Moreover, some characterizations and properties of this measure are shown by examples, which is every useful in future research works of generalized rough sets induced by a covering.