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.
Angilella et al. (Tue,) studied this question.