On generalized rough fuzzy approximation operators

This paper presents a general framework for the study of rough fuzzy sets in which fuzzy sets are approximated in a crisp approximation space. By the constructive approach, a pair of lower and upper generalized rough fuzzy approximation operators is first defined. The rough fuzzy approximation operators are represented by a class of generalized crisp approximation operators. Properties of rough fuzzy approximation operators are then discussed. The relationships between crisp relations and rough fuzzy approximation operators are further established. By the axiomatic approach, various classes of rough fuzzy approximation operators are characterized by different sets of axioms. The axiom sets of rough fuzzy approximation operators guarantee the existence of certain types of crisp relations producing the same operators. The relationship between a fuzzy topological space and rough fuzzy approximation operators is further established. The connections between rough fuzzy sets and Dempster-Shafer theory of evidence are also examined. Finally multi-step rough fuzzy approximations within the framework of neighborhood systems are analyzed.