Covering-Based Generalized Rough Fuzzy Sets

This paper presents a general framework for the study of covering-based rough fuzzy sets in which a fuzzy set can be approximated by some elements in a covering of the universe of discourse. Some basic properties of the covering-based lower and upper approximation operators are examined. The concept of reduction of a covering is also introduced. By employing the discrimination matric of the covering, we provide an approach to find the reduct of a covering of the universe. It is proved that the reduct of a covering is the minimal covering that generates the same covering-based fuzzy lower (or upper) approximation operator, so this concept is also a technique to get rid of redundancy in data mining. Furthermore, it is shown that the covering-based fuzzy lower and upper approximations determine each other

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