The Measures Of Fuzzy Rough Sets And Their Applications

The research on the measures of rough sets is one of research hot spots.In this paper,firstly,we introduce the measures of the rough sets into the fuzzy rough sets based on regular probability spaces,and summarize the properties of them.We get that these measures can be reduced to the inclusion degree.Secondly,we define the measures of the fuzzy rough sets based on regular probability spaces,including the belief and plausibility functions which can be used to describe the upper and lower approximation operators,and the accuracy measure of rough sets,degree of rough belonging and dependency function also are defined,these measures can be reduced to the inclusion degree,too.Finally,we defined the reduction of the information system based on the fuzzy rough sets by the dependency function.An example is employed to illustrate the definition of the reduction of the fuzzy rough sets.