A Novel Expanding-Window Tensor TOPSIS (EWTT) Approach for Dynamic Sustainability Ranking of Countries

This study proposes the Expanding-Window Tensor TOPSIS method, a novel dynamic multi-criteria decision analysis framework that integrates temporal feature extraction with an expanding-window estimation scheme. The method structures panel data as a third-order tensor and extracts three time-series features—linear trend, mean, and standard deviation—from rolling windows for each alternative-criterion pair. These features are retained as distinct dimensions of the decision matrix. At each target year, normalization bounds, entropy weights, and ideal solutions are calculated based on the information accumulated up to that year, thereby avoiding look-ahead bias. A burn-in threshold prevents unreliable early estimates, while complementary diagnostics assess the convergence of weights and sensitivity to the window width. The method yields a dynamic score matrix representing the evolution of the relative position of each alternative over time. The proposed framework is applied to the ND-GAIN Country Index, which includes data for 152 countries from 2000 to 2024. The dynamic rankings have high face validity, almost perfect robustness to the choice of window width and burn-in threshold, fast convergence of the entropy weights, and robustness to changes in the alternative set. Extensive robustness checks—including Monte Carlo weight-uncertainty analysis, comparisons with alternative weighting (CRITIC, standard-deviation-based, equal weighting) and aggregation (VIKOR) methods, and benchmarks against Dynamic TOPSIS-Entropy and a rolling-window variant—confirm the insensitivity of the findings to the choice of weighting and aggregation strategy. The methodology is not domain-specific and offers a transparent and diagnostically rich tool for dynamic performance evaluation.