Research on the fuzziness of rough set model based on compatible relation over double universes

According to the relation between two elements in different universes, a fuzzy compatible relation is established as a generalization of rough set model over two universes. Firstly, new fuzzy approximation operators are presented basing on a fuzzy set with parameter which is defined in this article. Meanwhile, several important properties and theorems are proved as well. Next, by using the calculations of elements in the fuzzy matrix, a more effective method to obtain the approximation sets is proposed. Finally, an example is applied to illustrate the significance of the model.