Abstract:Some scholars have already proposed a lot of dominance relation and corresponding rough models under incomplete information system in order to deal with the problem of preference decision which has incomplete information. It is uncertain that no matter use which method to contrast two objects as long as there is missing value. According to this defect, this article analyzes the factors that influence the gray scale, defines the concept of the gray and the difference coefficient in the dominance relation, and gives the calculation method and establishes an index to measure the degrees of the contrast between two objects. Therefore, the dominance relation based on grey system and its rough approximation model is presented. Through the comparison analysis, the precision and quality of the rough set model based on the grey dominance relation are improved. The given example proves the practicality and effectiveness of the grey dominance relation and its rough approximation model.