Dynamic evaluation of global sustainability: longitudinal ranking and spatial profiling across countries.

This study addresses the limitations of static evaluation models in global sustainability assessment by tracing longitudinal sustainability trajectories across 103 countries. We develop an integrated analytical framework that combines Dynamic TOPSIS with time-decayed entropy weighting to capture the temporal evolution of sustainability performance from 2014 to 2024. To enhance robustness, linear ranking results are cross-validated through non-linear spatial classification using K-means clustering with k-means + + initialization. Seven core indicators spanning economic, social, and environmental dimensions are employed to characterize the structural profiles of sustainability tiers. The results reveal a pronounced staircase effect in global sustainability, with countries converging into three stable tiers. The three-cluster solution is supported by a reduction in the Sum of Squared Errors from 26.34 to 8.06, with diminishing marginal improvements thereafter. Robustness tests show stable rankings, with no rank reversal among the top 20 countries and consistent positions within the top five. A notable gap is found in the Lagging Tier: despite relatively high environmental efficiency driven by low industrialization, sustainability progress is held back by weak human capital and institutional quality. The Leading Tier, by contrast, maintains balanced performance through sound governance and environmental management. By giving greater weight to recent observations through time-decayed weighting and cross-checking results through both linear and spatial methods, this study offers a dynamic alternative to static sustainability rankings. The findings point to education and governance gaps as key barriers in lower-tier nations, with implications for international interventions that go beyond purely economic assistance.