On a Choquet Integral DEA Cross-Efficiency Evaluation Method Involving the Satisfaction of Decision-Making Units and Weight Balance of Indicators

The secondary goal approach is an effective way to address the problem of the non-uniqueness of the optimal weights The secondary goal approach is an effective way to address the problem of the non-uniqueness of the optimal weights for decision-making units (DMUs) in the cross-efficiency evaluation process of data envelopment analysis (DEA). However, on the one hand, existing secondary-goal models seldom consider the willingness of DMUs to accept and be satisfied with the cross-efficiency evaluation results of DEA. On the other hand, the problem of zero weights and excessive differences of indicators has not been given enough attention. Furthermore, the traditional DEA approach ignores interactions between indicators. To overcome these problems, in the context of considering the interaction of input (or output) indicators, this study introduces the idea of the minimum dissimilarity of weights and constructs an improved method for evaluating the cross-efficiency of the secondary goal based on the DMUs' satisfaction. In this method, the 2-additive Choquet integral is used as a more feasible attempt to reflect the pairwise interaction between input (or output) indicators to improve the differentiation of DEA evaluation results. Additionally, the satisfaction targets of DMUs are adjusted according to the three ethical principles of fairness (fraternity), utilitarianism and equity in social choice theory to obtain a choice of optimal weights that is consistent with the values of individual DMUs. This paper validates the performance of the improved DEA method through comparative analysis of arithmetic cases. Then the method is applied to the study of the input-output efficiency assessment of the water-energy-food nexus in China.