为丰富水生态承载力研究方法，将加权 Bonferroni 算子（weighted?Bonferroni?mean，WBM）应用于水生态承载 力评价研究，构建相应的 WBM 评价模型。通过建立水生态承载力评价指标体系，运用层次分析法和改进熵权法 确定指标权重，再利用 WBM 评价模型进行承载力评价，并将其与广泛应用的 TOPSIS 模型评价结果进行对比，以 太原市为例对方法的可靠性进行验证，进一步采用障碍度模型识别影响水生态承载力的关键障碍因素。结果表 明：太原市 2009—2020 年水生态承载力状态于临界承载上下波动，整体变化趋势不显著，近年来呈良好态势发展； 水资源、水生态子系统承载状态波动较大；通过与 TOPSIS 模型对比，该评价模型评价结果较为一致，表明 WBM 模型适用于水生态承载力综合评价；制约该地区的障碍因素主要集中在水资源子系统。

Water ecological carrying capacity is a comprehensive concept based on the theory of carrying capacity, considering water resources, water environment, and other factors to study the water ecosystem. It is based on the principle of sustainable development, covering water resources and the water environment, emphasizing the sustainable carrying capacity of water ecosystem to human society and economy. At present, the evaluation methods of water ecological carrying capacity mostly referred to the research of water resources carrying capacity and water environment carrying capacity, including SD, fuzzy evaluation method, TOPSIS model, and so on. The Bonferroni mean operator proposed by Bonferroni can effectively capture the correlation between input variables and can aggregate multiple input variables into one input variable. It is an aggregation operator between the maximum and the minimum. This method eliminated the mutual influence and interdependence between variables through iterative operation so that the comprehensive evaluation results can be fair. In recent years, the Bonferroni mean had been well expanded and applied in practical problems such as multi-attribute comprehensive evaluation and group decision-making. Xia et. al introduced the weight vector of the variable into Bonferroni mean and proposed the weighted Bonferroni mean, which considered the relative importance of the variable itself. Try to weaken the influence of the correlation between indicators on the evaluation results of water ecological carrying capacity and enrich the research methods of water ecological carrying capacity, the weighted Bonferroni mean operator was employed in the evaluation system of water ecological carrying capacity, and a comprehensive evaluation model of water ecological carrying capacity-WBM evaluation model was established. Taiyuan City was taken as the research object to verify the reliability of WBM, to provide an alternative method for the evaluation of water ecological carrying capacity, and provide support for promoting regional ecosystem protection.Based on the framework of 'target layer-criterion layer-index layer', the index system of water ecological carrying capacity was established. The analytic hierarchy process and the improved entropy weight method were used to determine the subjective and objective weights of the indicators, and the combined weights of the indicators were obtained by the multiplication integration method. The weighted Bonferroni mean evaluation model was established to evaluate the dynamic change process of water ecological carrying capacity, and it was compared with the widely used and recognized TOPSIS model evaluation results. The key obstacle factors in the study area were identified by the obstacle degree model, and the applicability of the weighted Bonferroni mean model is analyzed.The evaluation index system and WBM model were applied to the evaluation of the water ecological carrying capacity in Taiyuan city. The results show that the water ecological carrying capacity in Taiyuan City fluctuates up and down in the critical overload state from 2009 to 2020. The overall trend of change was not obvious and had developed in a good way in recent years. For the four subsystems: The carrying capacity of water resources subsystem decreases from safe carrying capacity to severe overload, the carrying capacity of water environment subsystem increases from overload to optimal carrying capacity, the carrying capacity of water ecology subsystem fluctuates up, and down in the critical overload state, and the carrying capacity of water security subsystem decreases to critical overload. The water resources and water ecological subsystems had large fluctuations in their bearing status. The identification of the barrier factors showed that the barrier factors constraining the area were mainly concentrated in the water resources subsystem.In comparison with TOPSIS evaluation results, it can be seen that the weighted Bonferroni mean model was reasonable and reliable for water ecological carrying capacity evaluation. The above results showed that the proposed model was reasonable and reliable, and enriched the research results of quantifying the water ecological carrying capacity. This study provided an optional method to weaken the influence of correlation between indicators on the evaluation of water ecological carrying capacity and to objectively quantify the water ecological carrying capacity, but how to quantify the influence of correlation between indicators on the evaluation results needed further study.