结合粗集模糊熵和PCA载荷阵改进的TOPSIS方法  

Applying fuzzy entropy of rough set and PCA loading matrix to improvements of TOPSIS method

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：《计算机工程与应用》2011年第18期56-59,共4页Computer Engineering and Applications

基　　金：国家自然科学基金(No.60675031);国家重点基础研究发展规划(973)(No.2007BC311003);安徽省高等学校省级自然科学研究项目(No.KJ2008B093)~~

摘　　要：基于粗糙集属性的隶属函数,提出了利用指标公共因子的载荷矩阵和粗糙集的模糊信息熵两种方法,确定加权规范决策矩阵,选择出理想解和负理想解,计算现实中各方案与理想方案和负理想方案的距离;以此度量作为综合评估的标准,确定优劣进行决策。从统计学和信息学两方面对TOPSIS方法进行改进:在将原始变量转变为主成分的过程中,利用特征值与公共因子的载荷矩阵确定权重,反映了各个变量在公共因子上的相对重要性,克服了主观因素的影响,有助于保证客观地反映样本间的现实关系;如实度量属性本身信息量的大小,有效表达不同的属性面对不同的决策方案有不同的信息容量。算例结果显示由于后者侧重不同方案不同信息量,决策细节更为有效。Based on membership function of attribute in rough set,two methods of using loading matrix of common factors and fuzzy entropy of rough set are put forward to determine the weighted standard decision matrix,and then an ideal solution and a negative-ideal solution are chosen to calculate the distance between the alternatives in the reality and them.The measurement is regarded as a comprehensive evaluation criteria to determine which is optimal in all alternatives.TOPSIS method is improved from the two aspects of statistics and informatics,the former has determined the common factors which have an effect to all original variables in the process of the original variables transforming into principal components,using eigenvalues of principal components and loading matrix of common factors to definite weight,it reflects the relative importance of each variable to common factors,and overcomes the influence of subjective factors,the reality relations between the samples are reflected objectively.The latter has measured the information size of attribute truthfully,different attribute has dif- ferent information capacity for different decision scheme.

关 键 词：粗糙集 模糊信息熵 TOPSIS方法 载荷矩阵 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]