**5. Conclusions**

This study combines fuzzy-interval linear programming and dynamic programming to establish a fuzzy-interval dynamic programming (FIDP) method. The system uncertainty is expressed in the form of interval numbers in the model establishment and results presentation. In order to solve the conflicts among users caused by uneven distribution of resources, the FIDP model incorporates the overall satisfaction of users into the objective function in order to reflect fairness in the solution results. As for the dynamic variability, the FIDP model introduces dynamic programming to obtain the specific allocation schemes at different stages of the planning year. Therefore, the model is able to handle the problem of uneven resources allocation under uncertainty and dynamics.

In this paper, the water resources allocation under uncertainty and dynamics in Handan City is studied to verify the feasibility of the model. The solutions cannot only get the optimized target value in this area, but also get the specific water allocations and water shortages for each water user at different stages in the form of intervals, so that the government and users can adjust their strategies to deal with the crisis in time. In addition to the economic and environmental goals, the obtained solution also provides the satisfaction of water users by introducing a weight coefficient, which effectively alleviates the contradictions among users. Through model comparison, the FIDP is proved to be superior to FILP model in this area. Consequently, the developed FIDP model would be more rational and applicable for regional water allocation under uncertainty and dynamics, which is of great help to the sustainable development of the region.

**Author Contributions:** Conceptualization, M.S. and F.X.; methodology, M.S. and F.X.; writing—original draft preparation, M.S. and F.X.; writing—review and editing, M.S. and Y.F.; funding acquisition, M.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by Nation Natural Science Foundation of China (61873084), and Natural Science Foundation of Hebei, in China (D2019402235).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Acknowledgments:** The authors are grateful to the editors and the anonymous reviewers for their unique and profound comments and suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest.
