基于不完备信息系统的灰度优势粗糙近似模型

为解决不完备信息的偏好决策问题，多种优势关系及其相应的粗糙集模型被提出并证实其实用性. 然而在实际情况中，只要存在缺失值那么无论使用何种方法对比出来的优势关系都存在一定的不确定性. 基于此，本文分析了影响灰度大小的因素，定义了优势关系中灰度和差异系数的概念并给出了计算方法，建立了两对象间进行对比的灰度度量. 提出了基于灰度的优势关系及其粗糙集近似模型. 与广义扩展优势关系和扩展优势关系相比，基于灰度优势关系的粗糙集模型近似分类精度和质量均有提高. 最后通过实例证明了灰度优势关系及其粗糙近似模型的实用性.

Grey Rough Approximate Model Based on Incomplete Information System

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.