Coupling Symmetric Interaction Entropy and Connection Numbers: An Uncertainty-Informed Approach for Assessing Water Resource Spatial Equilibrium

Assessment of water resource spatial equilibrium (WRSE) is crucial for regional sustainable development, yet traditional methods always face difficulties in quantifying systemic differences and resolving their internal uncertainties. Accordingly, this study proposes a novel multi-attribute decision-making (MADM) model that integrates symmetric interaction entropy (SIE) with connection numbers (CNs) within a variable-weight framework. Firstly, information differences between alternatives and an ideal state were quantified by SIE, then these differences were decomposed into certain and uncertain components through the “identity–difference–opposition” (IDO) idea of CNs. In addition, a variable-weight mechanism was incorporated to enhance the model’s adaptability to regional characteristics. Applied to evaluate the WRSE in the Beijing–Tianjin–Hebei (BTH) region from 2014 to 2023, the model reveals that Hebei maintains the most favorable equilibrium state, with a partial identity potential or equal potential, followed by Beijing, while Tianjin predominantly exhibits partial opposite potential due to pronounced conflicts between its resource endowment and industrial structure. The proposed model not only enhances the sensitivity and interpretability of evaluation results but also facilitates the identification of key vulnerable indicators, thereby providing a scientific basis for formulating differentiated regional water governance strategies.