Type-2 fuzzy mixed-integer bi-level programming approach for multi-source multi-user water allocation under future climate change

Global climate change and increasing pressure of water shortage reinforce the necessity of optimal water management. In this study, a type-2 fuzzy mixed-integer bi-level programming (T2FMBP) approach is developed for the identification of reasonable water allocation policies by incorporating type-2 fuzzy sets, mixed-integer linear programming, bi-level programming and Stewart model into a general optimization framework. The T2FMBP model improves upon conventional bi-level programming for handling tradeoffs between two-level decision makers considering multiple water allocation processes. It is capable of addressing parameter uncertainties caused by natural conditions and human activities, and supporting in-depth analysis of water allocation schemes associated with future climate change. In this study, group opinion aggregation method for fuzzy number construction, critical value method for type-2 fuzzy number defuzzification, and fuzzy coordination method for solving bi-level programming are adopted. Then, the model was demonstrated for a real-world case study in the Zhanghe Irrigation District for multi-source multi-user water resources planning. The results show that the proposed model can tackle tradeoffs among hierarchical decision makers' conflicting concerns under uncertainties characterized as type-2 fuzzy numbers. Besides, the results can help generate water allocation schemes among different water sectors as well as different crop growth stages effectively under three hydrological years (wet year, normal year, and dry year) and three representative concentration pathway (RCP) scenarios (RCP 2.6, RCP 4.5, and RCP 8.5). Furthermore, comparison was made between T2FMBP model and four single-level models with same constraints. The comparison reveals that T2FMNP model considers all the targets and makes excellent balance between two-level decision makers. A comparison between current situation and RCP scenarios will help make policies for foresight. The formulated framework is applicable for similar regions to determine water strategies in a changing environment, thus promote sustainable development of socio-economic and water resources system.