Uncertainty of Multiple Granularity Rough Fuzzy Set Model
Aiming at the disaccord of the lower and upper approximations for covering rough set,a reasonable covering model is introduced.The structure and correlative property of this model is discussed and proved.The method of roughness measuring over the covering rough fuzzy set is defined.The maximum fuzzy set is presented and problem of equal roughness is solved by defining distance between fuzzy set and the maximum fuzzy set.Then the correlate notion of rough entropy is constructed and an example is given to show the validity of the method of this model.By proving theorem,the conclusion that measuring of rough degree and rough entropy are monotonously decreasing with the subdivision of covering sets is obtained.The theoretical evidence of measuring of uncertainty among rough sets,rough fuzzy set and coving rough set is provided.