The notion of roughness of a fuzzy set

The roughness of a set (according to the notion introduced by Pawlak in 1991) can be regarded as the MZ-distance between its upper and the lower approximations. With this idea in mind, we have generalized Pawlak's definition, by replacing the MZ-distance by a general “distance” measure. We also generalize the notion of roughness of fuzzy sets introduced by Huyhn and Nakamori in 2005.