基于前景理论和熵权法的交叉效率集结方法

Cross-efficiency Aggregation Method Based on Prospect Theory and Entropy Weight Method

传统的交叉效率集结过程通常采用算术平均方法,不仅会低估自评的重要性,而且未考虑决策者的风险偏好。针对上述问题,提出一种基于前景理论和熵权法的交叉效率集结方法。首先,求解交叉效率矩阵,运用熵权法确定他评过程中评价单元的指标权重。然后,引入前景理论以考虑决策者在交叉效率集结过程中的风险偏好,利用TOPSIS方法识别正负参考点,进而构造总体效用函数,得到前景交叉效率矩阵。随后,构建最大化前景价值模型,求解集结权重。该方法既考虑到交叉效率集结的相对重要性权重,又将决策者的风险偏好纳入到效率评价中,从而实现决策单元的全排序。最后,结合实例验证方法的有效性。

The traditional cross-efficiency aggregation process usually adopts the arithmetic mean method,which not only underestimates the importance of self-evaluation of decision-making units but also does not take into consideration the decision maker’s risk preferences.Given the above questions,this paper proposes a cross-efficiency aggregation method based on prospect theory and entropy weight method.Firstly,solve the cross efficiency matrix,and the entropy weight method is applied to solve the index weight of each evaluation unit in the peer evaluation process.Then,the prospect theory is introduced to reflect the risk preferences of decision-makers in the cross efficiency aggregation process,and the TOPSIS method is applied to identify positive and negative reference points,and then construct the overall utility function to obtain the prospect cross efficiency matrix.Subsequently,a model for maximizing the prospect value is constructed to solve the aggregation weight of cross efficiencies.This method not only considers the relative importance weights for cross-efficiency aggregation but also incorporates the risk preferences of decision-makers into the efficiency evaluation to realize the overall ranking of decision-making units.Finally,an example is given to illustrate the effectiveness of the method proposed.