This paper presents a new extension of fuzzy sets: R-fuzzy sets. The membership of an element of a R-fuzzy set is represented as a rough set. This new extension facilitates the representation of an uncertain fuzzy membership with a rough approximation. Based on our definition of R-fuzzy sets and their operations, the relationships between R-fuzzy sets and other fuzzy sets are discussed and some...

To keep the key idea of rough set and the representation of information in rough set theory, empty representation is processed properly and three new forms of rough approximation sets are defined as a generation of general binary relation based rough set model. Moreover, the properties of approximation operators in these new rough sets are discussed. The relations among them are studied in this...

Article history: Received 15 July 2009 Received in revised form 6 April 2010 Accepted 7 April 2010 Available online 9 April 2010

Soft rough sets which are a hybrid model combining rough sets with soft sets are defined by using soft rough approximation operators. Soft rough sets can be seen as a generalized rough set model based on soft sets. The present paper aims to combine the covering soft set with rough set, which gives rise to the new kind of soft rough sets. Based on the covering soft sets, we establish soft coveri...