A Hybrid Model with K-Means and ELECTRE-III to Analyze Countries Considering Prosperity Indicators

This article employs an original hybrid approach to evaluate countries, combining the K-means clustering algorithm with the ELECTRE-III multicriteria ranking method and Monte Carlo simulation. The aim is to rank representative alternatives constructed by the obtained clusters’ centroids and taking into account the results sensibility to uncertainties related to the parameters of the modelling. Therefore, besides grouping the alternatives into homogeneous categories, which not necessarily are ordered in terms of preference, our approach ranks these clusters. The approach is applied to a dataset with 12 indicators regarding a prosperity evaluation, namely the Prosperity Index from the Legatum Institute. The results include cluster visualizations, the preference relations defined by ELECTRE-III, and the resulting ranking. Furthermore, a subsequent analysis is presented using 10,000 simulations that consider variations in the ELECTRE-III parameters and the utilization of probability distributions in order to account for uncertainty. The results demonstrate consistency with expectations, and the robustness of the rankings is confirmed by the statistics obtained from the simulations.