On the Representation Theorems of Fuzzy Rough Sets

The upper and lower approximation operators of rough set were defined by dual form. The representation theorems for this kind of fuzzy rough sets were presented using cut set of relative fuzzy relation and fuzzy sets. It is proved that the upper approximation of such fuzzy rough set in a fuzzy approximation space is just its image derived according to generalized extension principle and binary fuzzy similar relation. It is also proved that ZadehK s fuzzy Compositional Rule of Inference (CRI) has the same form with the specific generalized extension principle, and the inference result can be obtained through it. Thus, fuzzy inference can be studied with the help of the properties of generalized extension principle and rough set theory.