A Bayesian Based Multi-stage Type-2-fuzzy Game and Interval-stochastic Programming Method for Planning Basin Energy-water-climate Nexus System

The contradiction between increasing energy demand, decreasing water availability, and deteriorating ecological environment indicates the urgent necessity for an energy-water-climate nexus management (EWCM) system. The contribution of this paper is to propose a posterior probability-based multi-stage cooperative game and type-2-fuzzy interval-stochastic programming model of the EWCM (PMCTFSP-EWCM) to determine the optimal solutions for sustainable development under ambiguities and uncertainties. The type-2-fuzzy sets and multi-stage interval-stochastic programming are combined to deal with objective and subjective uncertainties of partial parameters with flexible constraints. Moreover, multi-stage cooperative game was adopted to reflect the cooperation and competition between energy subsystem and water resources subsystem. Then, the model was applied to a case study to investigate the EWCM in the Yellow River Basin (YRB), China. Improving water availability satisfaction and feasibility degree can reduce external energy dependence costs from \(\left[84.9, 126.4 \right] \times 10^{9}{\$}\) $\left[84.9,,,126.4\right]\times {10}^9\mathrm{\$}$  to \(\left[ 12.7, 14.3 \right] \times 10^{9} {\$}\) $\left[12.7,,,14.3\right]\times {10}^9\mathrm{\$}$ . Furthermore, when considering the objective function of cost, target revenue functions, and corresponding constraints of the EWCM mutual feedback relationship, the proportion of fossil energy supply in the YRB was reduced to 63.28%-71.79%. These measures could reduce the generation of negative values, which has long-term significance for the healthy and sustainable development of EWCM.