An enhanced simulation-based approach for multicriteria evaluation of SMEs’ performance
本文扩展了sigma-mu效率分析，在仿真结果中不仅考虑均值和变异性，还纳入偏度和峰度，并使用灵活狄利克雷分布建模准则权重不确定性，基于2018-2022年欧洲中小企业数据验证了该方法能更全面比较备选方案，但也会削弱优势关系。
Abstract Stochastic multi-attribute acceptability analysis (SMAA) has become a popular tool for dealing with uncertainties in multi-criteria decision aid. SMAA relies on a simulation process to analyze the performance of a set of alternative options over multiple scenarios for the parameters of an evaluation model and/or the data. The sigma-mu efficiency analysis has been proposed to aggregate the simulation results through a data-driven process that relies on ideas from data envelopment analysis (DEA). In this paper, we extend the sigma-mu efficiency analysis considering not only the mean and the variability of the alternatives’ performance over the simulation scenarios, but also skewness and kurtosis. To model the uncertainty in criteria weights, we employ the flexible Dirichlet distribution, which allows the modeling of the variations in the relative importance of the evaluation criteria. The empirical findings, derived from a dataset of European small and medium-sized enterprises (SMEs) spanning from 2018 to 2022, show that incorporating kurtosis and skewness into the analysis enables a more comprehensive comparison of alternatives. However, this added depth also weakens the dominance relationships between alternatives when considering all four statistical moments.