Information-Theoretic Measure of Uncertainty in Generalized Fuzzy Rough Sets

Rough set theory has become well-established as a mechanism for uncertainty management in a wide variety of applications. This paper studies the measurement of uncertainty in generalized fuzzy rough sets determined by a triangular norm. Based on information theory, the entropy of a generalized fuzzy approximation space is introduced, which is similar to Shannon's entropy. To measure uncertainty in generalized fuzzy rough sets, a notion of fuzziness is introduced. Some basic properties of this measure are examined. For a special triangular norm T= min , it is proved that the measure of fuzziness of a generalized fuzzy rough set is equal to zero if and only if the set is crisp and definable.