A new cross-efficiency aggregation in data envelopment analysis: considering fairness mentality and group consensus

Cross-efficiency evaluation (CEE) is an effective tool for ranking decision-making units (DMUs). The traditional data envelopment analysis (DEA) model employs self-evaluation to measure the performance of DMUs. CEE, as an extension of the DEA, includes self-evaluation and peer-evaluation, assessing the overall performance of each DMU through its own weights and the weights of all DMUs. The current CEE, however, aggregates self-evaluation and peer-evaluation efficiencies mostly via the arithmetic average, which underestimates the importance of self-evaluation and ignores the subjective preferences of decision-makers as well. To address this deficiency, considering the fairness mentality of decision-makers, this paper first introduces the regret theory to depict the regret aversion of decision-makers, and proposes the fair regret cross-efficiency aggregation (FRCEA) method (Method 1). Then the upper and lower limits of the fair regret interval cross-efficiency (FRICE) are calculated, and parameters reflecting the preferences of decision-makers are introduced. Next, this paper puts forth a consensus cross-efficiency aggregation (CCEA) method (Method 2) based on the efficiency expectations of DMUs and the actual aggregation results. By creating a fair evaluation environment, this paper aims to enable all DMUs to participate in the efficiency evaluation and accept the results, reaching a final consensus. Finally, the effectiveness and rationality of the methods above are verified after evaluating the academic research efficiencies of 13 prestigious universities in China.