基于群决策考虑属性效用一致性的DEA他评交叉效率公共权重排序法

A common-weight ranking method for DEA peer-efficiency based on group decision-making and considering the consistency of attribute utility

针对数据包络分析(DEA)交叉效率方法大多是面向结果采用平均方式集结交叉效率,没有考虑评价过程中属性效用数据及其变动的特性,导致大量决策信息丢失、相对效率评价值与被评价决策单元的指标值关联性不够等问题,以交叉效率评价过程为导向,引入群决策理论,研究属性偏好及其属性效用变化特征,运用熵权法分析属性效用稳定性,发现评价中存在属性效用的熵及其熵权的唯一性性质,从而将各决策单元(DMU)的自评权重(个体偏好)集结为一个DEA评价系统的群权重(DEA系统偏好或群偏好),建立仅有一组公共权重的群决策他评交叉效率评价方法.该方法面向过程,依据他评交叉属性效用稳定性区分其在评价中的作用,用群决策他评交叉综合群效用替代交叉效率平均作为相对效率评价值,变结果导向的交叉效率集结为过程导向的权重偏好集结,实现将相对效率评价值与群权重和属性指标值直接关联.改进后的方法简洁直观,同时方便寻求改善相对效率的途径.最后,通过算例分析验证了所提出方法的可行性与有效性.

The additive mean mode is generally employed to aggregate efficiency in the traditional data envelopment analysis(DEA) cross efficiency method. However, this method does not take into account the characteristics of the attribute utility data and its variation, which may lead to the loss of decision information and insufficient correlation between the efficiency scores and attribute values. Oriented by cross efficiency evaluation process, the changing characteristics of attribute preference and attribute utility are analysed by introducing group decision-making theory. The uniqueness of the entropy and entropy weight of attribute utility is verified, which helps to aggregate DMU’s self-evaluation weight(individual preference) into group weight(DEA systematic or group preference) and forms a novel peer-efficiency evaluation method based on group decision-making with only a list of common weight. Considering the consistency of attribute utility, the average value of cross efficiency is replaced by the comprehensive group utility, which makes the aggregation object transform from cross efficiency to weight. This method realizes the direct correlation between efficiency scores and attributes values, and provides a path to improve relative efficiency. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.