基于信息熵的交叉环境DEA模型及其应用分析

Environmental Cross DEA Model based on Information Entropy and Its Application

传统DEA交叉评价方法,是将交叉评价矩阵中某一列(行)中的所有元素赋予相同的权重,然后进行简单的算术平均,得到综合评价分数。这种评价方法的缺点在于主观性过强且结果并不唯一。借鉴信息熵的概念,通过整个系统的信息构建熵距离,基于距离的大小给予矩阵中每一个评价单元动态权重,并证明这个权重为全域最优且唯一。最后,使用2012年北京市投入产出表的数据,以环境DEA模型的结果为基准,对比传统方法及改进型方法在结论上的异同并进行分析。

Traditional approach of cross-evaluation of DEA model is to give every element in cross evaluation matrix （CEM） equal weight, and calculate the simple average as the composite evaluation score. The drawback of this method is over objective and may lead the wrong conclusion due to the weights are not always unique. Therefore, we use information entropy to build the entropy distance based on the data of CEM, and propose a new model to calculate the weight in the matrix in a dynamic way. Moreover, we can prove that the new weight is globally optimal. Finally, by using the data of ＂2012 Beijing I--O table＂, we compare and analyze the different results of traditional and entropy based DEA model.