Question

# What is the difference between Fuzzy rough sets and Rough fuzzy sets?

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?

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.

20th Dec, 2014
Ganesan G
Rough Fuzziness: to be used when you plan to approximate a fuzzy input under crisp knowledge.
Fuzzy Roughness: to be used when you plan to approximate a fuzzy input under fuzzy knowledge.
5 Recommendations

20th Dec, 2014
Dr. Indrajit Mandal
Rajiv Gandhi Institute of Technology, Bangalore
Dear friend
Greetings
Both are one and the same.
I have used fuzzy rough sets in my papers. you may look at them.
I hope this helps.
Best regards
Dr.indrajit Mandal
20th Dec, 2014
Ganesan G
Rough Fuzziness: to be used when you plan to approximate a fuzzy input under crisp knowledge.
Fuzzy Roughness: to be used when you plan to approximate a fuzzy input under fuzzy knowledge.
5 Recommendations
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.
You could find more details in below links;
Sincerely,
or
1 Recommendation
11th Mar, 2016
Soumen Ghosh
The University of Queensland
Rough-Fuzzy Set: Approximation of a fuzzy set in a crisp approximation space.
Fuzzy-Rough Set: Approximation of a crisp set in a fuzzy approximation space.
25th Jun, 2016
Tarik A. Rashid
University of Kurdistan Hewlêr (UKH)
11th Mar, 2018
Liang Zhou
University of Electronic Science and Technology of China
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.
1 Recommendation
18th Jul, 2019
Saqib mazher Qurashi