Question
Asked 25th Apr, 2018

When should one use Fuzzy set theory and Rough set theory? Is there any clear-cut line of difference between them?

Fuzzy set theory; Rough set theory; Applicability of set theory; Machine learning

Most recent answer

3rd May, 2018
Sandipan Karmakar
Xavier Institute of Management, Bhubaneswar (XIMB)
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.
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Popular Answers (1)

3rd May, 2018
Sandipan Karmakar
Xavier Institute of Management, Bhubaneswar (XIMB)
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.
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All Answers (4)

26th Apr, 2018
Mohamed-Mourad Lafifi
Badji Mokhtar - Annaba University
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 ...
- Fuzziness, uncertainty and vagueness - Theory and Logic Group
- What is the difference between Fuzzy rough sets and Rough...
Best regards
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26th Apr, 2018
Igor Gazdík
Independent Researcher
A rough set is an >>approximation<< of a crisp set by means of two sets which, respectively, represent the lower and the upper approximation of the original set. The approximation sets, in general, are crisp sets, but can also be fuzzy.
A fuzzy set in X is a collection of ordered pairs of x and mu(x), where x belongs to X (a collection of x), and mu(x), extending from 0 to 1, is the membership function of x.
The distinction between a rough set and a fuzzy set is that the rough set makes it possible to approximate the original crisp set by reducing it to the upper and the upper approximation. A fuzzy set, on the other hand, is a set the boundaries of which are not sharp (i.e. they are "fuzzy").
3 Recommendations
26th Apr, 2018
WOJCIECH BORKOWSKI
University of Warsaw
I have nothing to add to theory, but if you are interested in example in biology see:
1 Recommendation

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