The cross-regional environmental collaborative governance capability evaluation problem is a heterogeneous multi-attribute decision-making problem. In response to this problem, this paper first constructed a cross-regional environmental collaborative governance capability evaluation index system, including five dimensions, involving 25 specific indicators with heterogeneous multi-attribute characteristics. Then it designed a heterogeneous multi-attribute decision-making model to calculate the relative closeness, and then used closeness to construct a value function to determine the weight index of each attribute. Finally, an empirical study was conducted on the urban agglomeration in Beijing-Tianjin-Hebei region of China. After years of environmental governance, the Beijing-Tianjin-Hebei region has gradually formed comprehensive environmental management measures against air pollution, water pollution, solid waste pollution and ecological environmental damage. Using the data of 13 cities from 2010 to 2018, the weight calculation and comprehensive index calculation of the environmental collaborative governance capability index of China's Beijing-Tianjin-Hebei regional urban agglomeration were carried out. The evaluation methods and results provide a scientific basis for the selection of comprehensive governance measures for cross-regional environmental collaborative governance.
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