The sustainability evaluation using SDG indicators under a geometric integrated threshold score framework

Evaluating national sustainability requires frameworks that integrate diverse indicators, yet traditional compensatory methods often allow strong performance in one area to offset critical weaknesses in others, potentially distorting policy interpretation. To address this limitation, this study proposes the Geometric Integrated Threshold Score (GITS), a non-compensatory framework that integrates multiplicative aggregation of multiple geometric distances with threshold-based veto logic. This design effectively eliminates underperforming alternatives while preserving interpretability. Using longitudinal data from 2019 to 2023 across six core SDG indicators for 25 countries, we compare GITS and its soft-veto extension (GITS-S) with three benchmark models including the Sustainability Composite Score (SCS), the Elimination and Choice Expressing Reality (ELECTRE) III and Fuzzy ELECTRE III. Results show that under the strict hard-veto logic, only 7 out of 25 countries fully satisfied all baseline thresholds, resulting in nullified scores for the remaining 18 countries. The soft-veto extension (GITS-S) effectively resolves this issue by differentiating rankings among near-compliant countries, thereby clarifying its systematic distinctions from both compensatory and outranking approaches. Overall, GITS provides a unified, interpretable, and threshold-sensitive framework that supports more robust sustainability planning and policy prioritization.