ABSTRACT
Rough set theory and fuzzy set theory are extensions of classical set theory, and they are related but distinct and complementary theories. Rough set theory is mainly focused on crisp information granulation and its basic concept is indiscernibility (e.g., an indiscernibility between dierent objects deduced by different attribute values of described objects in the information system), whereas fuzzy set theory is regarded as a mathematical tool for imitating the fuzziness in the human classication mechanism, which mainly deals with fuzzy information granulation. Because of its simplicity and similarity with the human mind, its concept is always used to express quantity data expressed by language and membership functions in the intelligent system. In fuzzy sets, the attribution of elements may be between yes and no. Let us take the example of a beautiful scenery; we cannot simply classify the beautiful scenery into a category between yes and no. For the set of beautiful scenery, there does not exist good and de- nite border. Fuzzy sets cannot be described with any precise mathematical formula, but it is included in the physical and psychological process of a human’s way of thinking, because the physiology of human reasoning never uses any precise mathematical formula during the physical process of reasoning, and fuzzy sets is important in pattern classication. Essentially, both these theories study the problem of information granularity. e rough set theory studies rough nonoverlapping type and the rough concept, while the fuzzy set theory studies the
fuzziness between overlapping sets, and these naturally lead to investigating the possibility of the “hybrid” between the rough set and the fuzzy set.
