Regret cross-efficiency evaluation using attitudinal entropy approach

Data Envelopment Analysis (DEA), a nonparametric method for measuring the relative efficiency of DMUs, suffers from limitations such as efficiency overestimation and incomplete ranking of efficient DMUs. Cross-efficiency evaluation, combining self-evaluation and peer-evaluation, addresses these shortcomings but faces challenges due to non-unique optimal weights and the limitations of using simple arithmetic mean for aggregation. Existing secondary goal models, such as aggressive and benevolent models, often focus on extreme efficiencies and don't fully capture the complexity of individual decision-making under bounded rationality. This paper introduces a novel cross-efficiency model, RACE, to overcome these limitations.

The paper reviews existing DEA and cross-efficiency evaluation methods, highlighting their strengths and weaknesses. It discusses the development of secondary goal models to address the issue of non-unique optimal weights, including aggressive, benevolent, and neutral models. Various weight aggregation methods, such as those using cooperative game theory, order priority models, and entropy methods, are examined. The paper also reviews the application of regret theory and prospect theory in decision-making and cross-efficiency evaluation, emphasizing the importance of incorporating bounded rationality into these models.

The RACE method introduces a novel secondary goal model that considers both endogenous and exogenous reference points, incorporating the concepts of regret and rejoice from regret theory. The model uses utility functions for input and output attributes, incorporating risk aversion parameters. A regret-rejoice function is defined to capture individuals' emotional responses to outcomes relative to reference points. The attitudinal entropy approach is employed for weight aggregation, considering the decision-maker's preference for information uncertainty. The methodology involves several steps: 1) constructing a cross-efficiency matrix based on the regret theory model; 2) calculating the attitudinal entropy value for each DMU; 3) obtaining weight coefficients; and 4) synthesizing comprehensive cross-efficiency values. The model incorporates parameters such as risk aversion (a, b), regret aversion (δ), endogenous preference (λ), rejoice preference (ζ), and information preference (α, β) to capture individual decision-making characteristics.

The paper applies the RACE method to evaluate the efficiency of R&D activities in the high-tech industries of 12 Chinese provinces, using personnel and funding as inputs and number of inventions and sales revenue as outputs. The results are compared with those of traditional DEA models (CCR, aggressive, benevolent) showing that RACE results generally fall between the aggressive and benevolent model results. Sensitivity analysis reveals the impact of various parameters (α, β, δ, λ, ζ) on the efficiency scores, highlighting the importance of considering individual preferences. A comparison with other advanced cross-efficiency models (PCE, Wu's model, RCEC) using data on 13 Chinese universities further demonstrates RACE's effectiveness. RACE generally yields higher efficiency values and better discriminates among DMUs than the comparison models. Spearman rank correlation analysis shows high correlation with RCEC and Wu's models. The analysis of mean efficiency, IQR, and SD indicates RACE's strong discriminatory power, particularly for middle-performing DMUs, while maintaining relatively stable evaluations for extreme DMUs.

The findings demonstrate the advantages of the RACE model in addressing the limitations of traditional cross-efficiency evaluation methods. By incorporating bounded rationality, considering both endogenous and exogenous reference points, and using attitudinal entropy for weight aggregation, RACE produces more realistic and robust results. The parameter sensitivity analysis reveals the importance of understanding individual preferences in efficiency evaluations. The comparison with existing models highlights RACE's effectiveness in ranking DMUs and provides valuable insights into the relative strengths and weaknesses of different approaches. The study's results have implications for various fields, including financial investment, business management, and public project evaluation.

The RACE model offers a significant improvement in cross-efficiency evaluation by incorporating regret theory and attitudinal entropy. It provides a more comprehensive and realistic framework for evaluating DMUs, considering the bounded rationality of decision-makers and their individual preferences. Future research could focus on extending the model to incorporate interval numbers and dynamic evaluations.

The RACE model relies on fixed reference points, which may limit its flexibility. The model is also based on a static analysis framework and may not fully capture the dynamic nature of real-world decision-making. Future research could explore more flexible reference points and incorporate dynamic evaluations.