DEA Cross-Efficiency Evaluation Considering Interval Efficiency with Aggressive–Benevolent Formulation

In DEA cross-efficiency, information aggregation of self-evaluation and peer-evaluation has been one of the main concerns. The inherent variability of decision-makers’ preferences in peer-evaluation, whether expressed aggressively or benevolently within the secondary goal programming, can yield divergent peer-efficiency scores. Therefore, interval efficiency for considering different preferences of decision-makers and group opinions is used to represent the variable efficiency range. In this paper, comparison norms for the advantage degree between any two interval efficiencies are defined, and a pairwise advantage-degree matrix is developed. By aggregating this matrix through a dominance score, a unique ranking of DMUs can be obtained. Subsequently, a synthetic evaluation model, ICE-AB, is proposed for DEA cross-efficiency evaluation. To demonstrate the effectiveness, discriminatory capability, and practical applicability of ICE-AB, a benchmark numerical example, a differentiating numerical case, and an empirical application to major Chinese new energy vehicle manufacturers are provided. Comparative analysis and ranking results show that the new model not only preserves different peer-evaluation information but also obtains the unique ranking results of DMUs under uncertain attitudes of decision-makers.