基于证据推理和前景理论的交叉效率排序方法研究

针对由交叉效率评价策略和交叉效率集结方法的多样性而造成评价结果不一致的问题，提出利用证据推理方法和前景理论，综合各个交叉效率评价策略的评价结果，实现对决策单元的统一评价。首先，分别将选用的交叉效率评价策略以及各个评价策略中的他评效率设置成一级指标和二级指标，依据算数平均和前景理论分别确定一、二级指标的权重；其次，依据他评效率确定二级指标置信度，利用证据推理方法将各个交叉效率评价策略的他评效率综合转换成决策单元被评价为有效的置信度。决策者可通过比较决策单元被识别为有效的置信度的大小来判断决策单元交叉效率的大小，进而实现对决策单元的排序；最后，通过案例验证和说明本文提出方法的有效性和实用性。

Study on Cross-efficiency Ranking Based on Evidential Reasoning and Prospect Theory

There has a lot of researches on cross-efficiency based on data envelopment analysis (DEA), and different DEA cross-efficiency models usually lead to different decision making units (DMUs) rankings and conclusions. To avoid the biased performance evaluation caused by biased DEA cross-efficiency model and make a comprehensive assessment on DMUs, an alternative combined with prospect theory and evidential reasoning approach is proposed to integrate the cross-efficiencies of DMUs, which are obtained from several DEA cross-efficiency models, and the cross-efficiencies are converted into the belief degree to support the evaluated DMU being efficient. The weights of integrated efficiencies are obtained by prospect theory, which considers the expected gains and loss of decision makers. The rankings and comparisons of DMUs are determined by the final belief degrees. The higher the belief degree is, the better the DMU ranks. An assessment of 7 departments in a university is made with the proposed approach. It is found that the proposed approach integrates the evaluations of DMUs under aggressive, benevolent and neutral cross-efficiency models well, and leads a comprehensive conclusion.