In uncertainty models, there are models like Fuzzy model, Rough model and so on. But some papers use hybrid model naming as Fuzzy rough and Rough Fuzzy, so I like to know what is the differences between them?
As professor Ganapathy Ganesan has mentioned , Here is a conceptual difference between fuzzy rough set model and rough fuzzy set, we all know rough set deals with indiscernible elements and fuzzy set with fuzzy sets and memberships,
it is better to use rough fuzzy set modelling, when we have specified knowledge concepts but approximated concepts are not so clear (ill definition), and when problem knowledge is fuzzy concepts and approximated concepts are specified we could use fuzzy rough modelling.
The Fuzzy set means that the elements in a set are not determinative or changing by the observer. The Rough set means that the boundary of set congtaining some elments are not determinative or changing by the observer. The Classical set are that both the elements in the set and the boundary of the set determinative.
A rough fuzzy set is a pair of fuzzy sets resulting from the approximation of a fuzzy set in a crisp approximation space, and a fuzzy rough set is a pair of fuzzy sets resulting from the approximation of a crisp set in a fuzzy approximation space.
Fuzzy set works on features of the data whereas rough set works on attribute set of the data (crisp). Therefore, the result of rough-fuzzy hybridization set is the approximation of fuzzy input into crisp approximation space. On the other hand, fuzzy-rough set refers the approximation of crisp set into fuzzy approximation space.