Fuzzy set theory; Rough set theory; Applicability of set theory; Machine learning
Rough and Fuzzy set are almost same application wise. But theoretically they are different which makes Rough Sets superior than Fuzzy (Personal Opinion). Let me explain why theoretically Rough is better than Fuzzy. Fuzzy set starts with identifying a membership function a-priori and tries to fit the data in its theory, whereas Rough Set starts with no such assumption on membership function. Rough sets straightway starts fitting the data blindly from which membership function values are computed. This is why Rough sets make better explanation of uncertainty as it mimics what the data speak. As per my opinion Rough set is better suited in case of data science where prior information and knowledge about the process under consideration are not available and the analysts have to rely purely on the data.
Dear Sobhan,
Theories of fuzzy sets and approximate sets are generalizations of classical set theory to model inaccuracy and uncertainty; they are related but distinct and complementary theories. Both theories model different types of uncertainty. The rough set theory takes into account the Indiscernibility between objects. Indiscernibility is typically characterized by an equivalence relation. Rough sets are the approximation results of raw sets using equivalence classes. Fuzzy sets theory deals with the bad definition of the boundary of a class by a continuous generalization of the defined characteristic functions. Indiscernability between objects is not used in fuzzy set theory. A fuzzy set can be considered a class with fuzzy boundaries, while an approximate set is a raw set that is roughly described.
For more details and information about this suject please take a look at links in topic.
- Characterization of rough set approximations in Atanassov ...
https://www.sciencedirect.com/science/article/pii/S089812211100397X
- Fuzziness, uncertainty and vagueness - Theory and Logic Group
https://www.logic.at/lomorevi/LoMoReVI/transvague.pdf
- What is the difference between Fuzzy rough sets and Rough...
https://www.researchgate.net/.../What_is_the_difference_between_...
Best regards
I have nothing to add to theory, but if you are interested in example in biology see:
Article Rough sets in floristic description of inner-city of Warsaw
Rough and Fuzzy set are almost same application wise. But theoretically they are different which makes Rough Sets superior than Fuzzy (Personal Opinion). Let me explain why theoretically Rough is better than Fuzzy. Fuzzy set starts with identifying a membership function a-priori and tries to fit the data in its theory, whereas Rough Set starts with no such assumption on membership function. Rough sets straightway starts fitting the data blindly from which membership function values are computed. This is why Rough sets make better explanation of uncertainty as it mimics what the data speak. As per my opinion Rough set is better suited in case of data science where prior information and knowledge about the process under consideration are not available and the analysts have to rely purely on the data.
- Badges
- Science topic