Clustering and Ranking Countries Based on the Human Development Index Using Gaussian Mixture Models and Multi-Criteria Decision-Making Methods

The Human Development Index (HDI) is one of the most widely used composite indicators for evaluating national development. However, its reliance on fixed normalization bounds and equal weighting across dimensions may limit its ability to capture latent heterogeneity in development structures. To address these limitations, this study proposes a data-driven evaluation framework that integrates Gaussian Mixture Models (GMM) with objective multi-criteria decision-making (MCDM) methods. Using the 2023 HDI dataset reported in the 2025 Human Development Report, countries are first probabilistically clustered through GMM without imposing predefined development thresholds. The model identifies four statistically distinct development clusters characterized by heterogeneous health, education, and income profiles. Within each cluster, criterion weights are computed using the Criteria Importance Through Intercriteria Correlation (CRITIC) method to allow cluster-sensitive importance structures. Countries are subsequently ranked using multiple objective MCDM methods (Combinative Distance-based Assessment (CODAS), Combined Compromise Solution (CoCoSo), and Weighted Euclidean Distance Based Approximation (WEDBA), and final rankings are aggregated via the Borda Count approach to improve the stability and reliability of the rankings. The results reveal substantial reassignments relative to conventional HDI groupings and highlight structural mismatches between income level and overall human development performance. By combining probabilistic clustering with multi-method ranking, the proposed GMM–MCDM architecture provides a transparent and scalable decision-support framework for composite index evaluation. The framework is generalizable to other socio-economic performance assessment problems where latent structural heterogeneity and multi-criteria ranking are simultaneously required.