模糊粗糙集的表示定理

On the Representation Theorems of Fuzzy Rough Sets

通过对偶方式定义了模糊集的上、下近似算子,给出了模糊粗糙集在相应的模糊关系及模糊集的截集下的表示定理,证明了这种模糊粗糙集关于模糊近似空间的上近似恰为其在二元模糊相似关系下导出的广义扩张原理之下的像。证明了Zadeh模糊推理合成规则(CRI)与特定的广义扩张原理具有相同的形式,推理结果也可由此获得,这样可借助广义扩张原理的性质及粗糙集理论研究模糊推理.

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.