基于误差传递和熵的区间DEA方法

传统的DEA(data envelopment analysis)模型只能用来处理精确数据,而在现实生活中,由于统计误差、信息不完全等原因,获取精确数据十分困难,数据往往只能以区间数的形式给出.因此,如何在不确定条件下利用DEA方法评价决策单元的相对效率一直是DEA理论的研究前沿.针对这一问题,文章在DEA传统模型的基础上,利用改进的交叉效率思想,使用误差传递和熵处理区间数据,求得每个决策单元全局交叉效率的误差分布形式(中点值和误差最大估计值),然后根据全局交叉效率,使用有向距离指数给决策单元排序.最后通过两个算例来说明本文提出的方法的可行性和有效性.

Dealing with interval DEA based on error propagation and entropy

The conventional data envelopment analysis (DEA) measures the relative efficiencies of a set of decision making units (DMUs) with exact data of inputs and outputs. In the real world, however, it is possible to obtain interval data rather than exact data because of various limitations, e.g., statistical errors and incomplete information. To overcome those limitations, researchers have proposed kinds of approaches dealing with interval data envelopment analysis (DEA), which either use traditional data envelopment analysis (DEA) models by transforming interval data into exact data or get an efficiency interval by using the bound of interval data. In contrast to the traditional approaches above dealing with interval data envelopment analysis (DEA), the paper focuses on interval data envelopment analysis (DEA), combining conventional data envelopment analysis (DEA) models with error propagation and entropy, using the idea of modified cross efficiency, then gets the overall cross efficiency of decision making units (DMUs) in the form of error distribution and ranks decision making units (DMUs) using the calculated overall cross efficiency by the directional distance index. At last two numerical examples are employed to illustrate the feasibility and effectiveness of the proposed method.