基于粗集优势关系的属性赋权相对熵优化模型  

Optimal Attribute Weighting Relative Entropy Model Based on Dominance Relation in Rough Set

作　　者：毛军军[1,2] 李侠[1] 吴涛[1,3] 

机构地区：[1]安徽大学数学科学学院,合肥230039 [2]安徽大学计算智能与信号处理教育部重点实验室,合肥230039 [3]南京大学计算机软件新技术国家重点实验室,南京210093

出　　处：《计算机工程》2011年第15期125-127,共3页Computer Engineering

基　　金：国家自然科学基金资助项目(60675031);中国博士后科学基金资助项目(20070411028);安徽省高等学校省级自然科学研究基金资助项目(KJ2008B093);安徽省高等学校青年基金资助项目(2011SQRL186);安徽大学学术创新团队基金资助项目(KJTD001B)

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。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 analvsis result indicates the validitv and efficiencv of the model.

关 键 词：粗糙集 优势关系 属性依赖度 粒度 相对熵 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]