A comparative study of fuzzy sets and rough sets
The paper reviews and compares theories of fuzzy sets and of rough sets. Two formulations of fuzzy sets, viz., in terms of many-valued and of modal logics are considered. In both cases, the theory of fuzzy sets may be viewed as a deviation from classical set theory. Rough sets are considered from the operator-oriented standpoint, based on the notions of lower and upper approximations, and from the set-oriented one, where the notion of rough membership function is fundamental. In the latter case, fuzzy and rough sets are closely related since rough membership functions are special fuzzy membership functions. In the operator-oriented approach, the theory of rough sets is an extension of classical set algebra with a pair of additional operators. Finally, combinations of fuzzy and rough sets are considered. Among others, interval fuzzy sets are defined both for modal-logic-based fuzzy sets and the set-oriented view of rough sets.
scientific article; zbMATH DE number 1326010
scientific article