A rough membership function may be interpreted as a special kind of fuzzy membership function. Under this interpretation, is it possible to re-express the standard rough set approximations, and to establish their connection to the core and support of a fuzzy set
but what is the weakness and strengths of this model?
Rough sets and fuzzy sets are two distinct (but complementary) approaches to data modelling as a result of uncertainty in knowledge. The advantages are that one potentially has the ability to model two different types of uncertainty; indiscernibility for rough sets and vagueness for fuzzy sets.
Many of the characteristics of the hybridisation (fuzzy and rough) depends on which interpretation you use. It is important to note of course that rough-fuzzy sets and fuzzy-rough sets are two different things. A fuzzy-rough set can be defined in a number of ways, but should always collapse to a rough set when all of the objects under consideration are crisp or discrete. Have a read of Dubois and Prades seminal work in this area, it will provide much more detail.
Dubois, Didier, and Henri Prade. "Putting rough sets and fuzzy sets together." Intelligent Decision Support. Springer Netherlands, 1992. 203-232.
The advantages of fuzzy rough set hybrid model, it can deal hybrid decision systems (datasets). The weakness is required high computation time.
Both maintain some similarities, althoug roogh set are computational expensive
They are two different approaches to vagueness and uncertainity. The Fuzzy set, objects are assigned a membership function which assigns a membership value between 0 and 1. This value precisely describes whether the object possibly belongs to a set or it is rarely related. While, Rough set theory does not have the membership concept and classify each object through boundary region analysis. If the boundary is empty, then it is crisp set and all the objects belong to the set with probability 1 but if boundary is non-empty then the set is rough.
Rough set don't handle data belong to quantitative, where as fuzzy set don't handle data belong to qualitative. These are drawbacks of rough set and fuzzy set.
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