摘要： 针对传统粗集理论中属性赋权不一致，甚至相悖的问题，把2个概率分布的相对熵扩展到任意2个单维向量的相对熵，并将相对熵视作一种距离。通过定义属性重要度的代数观和粒度观确定优化权重的取值范围，根据各方案的属性值尽可能靠近理想值、远离负理想值的原理，建立单目标赋权优化模型。针对等价关系的局限性，将优势关系引入属性权重确定方法中。基于优势关系的序信息系统，将代数观下和粒度观下的权重通过相对熵优化模型进行耦合，得到多属性决策中属性权重的优化解。算例分析结果证明了该模型的有效性。

关键词: 粗糙集, 优势关系, 属性依赖度, 粒度, 相对熵

Abstract: Aiming at the difference and antinomy of the weighting in the rough set, the relative entropy of two probability distributions is extended to the relative entropy of two one-dimension vectors. The relative entropy is viewed as a distance measurement. The values range of optimal weights are determined by determinations of attribute importance in algebra view and knowledge granularity view respectively, and a single objective optimization model is established on the grounds that attribute values of alternatives are far away from negative ideal values and as close as to ideal values. On the other hand, since the limitation of equivalence relations, dominance relations are introduced to the method of determining the attribute weights. The weights in algebra view and knowledge granularity view are carried on the organic integration by the relative entropy optimization model based on dominance relations, in order to obtain optimal solution of the attributes in Multiple Attribute Decision Making(MADM). The analysis result indicates the validity and efficiency of the model.

Key words: rough set, dominance relation, attribute dependency, granularity, relative entropy

中图分类号: 

• TP18