A multi-weight fuzzy Methodological Framework for Allocating Coalition Payoffs of Joint Water Environment Governance in Transboundary River Basins

To ensure transboundary river basins are protected as a system, forming water environment governance coalitions is important. However, accurate determination and allocation of the payoffs of joint environment governance under uncertain conditions is a challenging task. This study used a triangular fuzzy number to describe the payoff and solve the fuzzy allocation problem. The article also considered the importance of different coalitions and the effectiveness of the distribution. In addition, the authors constructed a multi-weight fuzzy allocation quadratic programming model and proposed an analytical solution to determine the triangular fuzzy allocation payoffs. These contributions were used to allocate the coalition payoff of basin-wide environment governance, and the Zhanghe River Basin is used as a case study. The results showed that the model produces outputs comparable with the Shapley value allocation method. Therefore, the proposed methodological framework can be used as an alternative allocation scheme that provides a reasonable solution during uncertainty.