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Generalized fuzzy rough sets. (English) Zbl 1019.03037

Summary: This paper presents a general framework for the study of fuzzy rough sets in which both constructive and axiomatic approaches are used. In the constructive approach, a pair of lower and upper generalized approximation operators is defined. The connections between fuzzy relations and fuzzy rough approximation operators are examined. In the axiomatic approach, various classes of fuzzy rough approximation operators are characterized by different sets of axioms. Axioms of fuzzy approximation operators guarantee the existence of certain types of fuzzy relations producing the same operators.

MSC:

03E72 Theory of fuzzy sets, etc.
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