Generalized Rough Fuzzy Sets Based on Soft Sets

Dubois and Prade (1990) introduced the lower and upper approximations of fuzzy sets in a Pawlak approximation space, which initiated the concept of rough fuzzy sets. The present paper aims to combine the theories of fuzzy sets, rough sets and soft sets together. We consider the lower and upper approximations of fuzzy sets in terms of soft sets, which give rise to the new concepts of soft-rough approximations and soft-rough fuzzy sets extending Dubois and Prade's rough fuzzy sets.