Fuzziness based on covering generalized rough sets

The uncertainty measurement of rough sets is one of the key problems in the rough set theory. The rough membership function provides a new interpretation for rough sets and serves as an approach for measuring their uncertainty. This paper presents a novel measure of fuzziness based on covering generalized rough sets and its properties. We define the rough membership function for the fourth type of covering generalized rough sets and prove some relevant properties, and then the fuzziness is defined based on the proposed rough membership function. A specific example is illustrated to explain the fuzziness. Last, we put forward a reasonable rough membership function for the fuzziness of irrationality of the third type of covering generalized rough sets.