This study presents a credibility-based interval multi-objective crop area planning model for agricultural and ecological management under uncertainty. The model is developed through the integrations of interval multi-objective programming and fuzzy credibility-constrained programming by considering economic and ecological benefits of the study system, and dealing with interval and fuzzy uncertainties. It focuses on crop area optimization with the interval objective function of maximizing the system benefits, maximizing the watershed area, and fractional interval objective function of maximizing the land productivity (i.e., system benefits per unit area). Additionally, the relationship between watershed area and ecological discharge is expressed as interval linear function, which is estimated by using interval regression analysis method. Then, the model is applied to a case study in Minqin County in the lower reaches of Shiyang River Basin for crop area optimization in view of the increasing shortage of water resources and the competition between agricultural and ecological water use. Optimal solutions for different scenarios can be generated based on fuzzy credibility constraints when the predefined credibility levels are set as 0.6, 0.7 and 0.8, 0.9, respectively. The results show that the crop area optimization model can better balance the regional agricultural and ecological benefits while ensuring grain production and promoting water saving. Moreover, a higher level of credibility corresponds to a lower system benefit but a larger watershed area. When credibility level is raised from 0.6 to 0.9, the upper bounds of system benefits are decreased from 13.87$\times {10}^8$ Yuan to 13.81$\times {10}^8$ Yuan whereas the watershed area is increased from 41.01 km² to 42.12 km². These various optimal results can help decision makers weigh system benefits and constraint-violation risks. Therefore, the results of the model can provide decision-making basis for the crop area optimization and provide valuable basis for the sustainable development in Minqin County and similar study areas.

本研究提出了一种基于可信度的区间多目标作物面积规划模型，用于不确定条件下的农业和生态管理。该模型是通过区间多目标规划和模糊可信度约束规划的集成，考虑研究系统的经济和生态效益，处理区间和模糊不确定性而开发的。它侧重于作物面积优化，区间目标函数为系统效益最大化，流域面积最大化，部分区间目标函数为土地生产力（即单位面积的系统效益）最大化。此外，流域面积与生态流量的关系用区间线性函数表示，采用区间回归分析方法进行估计。然后，以石羊河流域下游民勤县为例，针对水资源日益短缺、农业用水与生态用水竞争的情况，将该模型应用于作物面积优化。当预定义的可信度分别设置为 0.6、0.7 和 0.8、0.9 时，可以基于模糊可信度约束生成不同场景的最优解。结果表明，作物面积优化模型在保证粮食生产和促进节水的同时，可以更好地平衡区域农业和生态效益。此外，较高的可信度水平对应于较低的系统收益但较大的流域面积。当可信度从 0.6 提高到 0.9 时，系统收益的上限从 13.87 降低 当预定义的可信度分别设置为 0.6、0.7 和 0.8、0.9 时，可以基于模糊可信度约束生成不同场景的最优解。结果表明，作物面积优化模型在保证粮食生产和促进节水的同时，可以更好地平衡区域农业和生态效益。此外，较高的可信度水平对应于较低的系统收益但较大的流域面积。当可信度从 0.6 提高到 0.9 时，系统收益的上限从 13.87 降低 当预定义的可信度分别设置为 0.6、0.7 和 0.8、0.9 时，可以基于模糊可信度约束生成不同场景的最优解。结果表明，作物面积优化模型在保证粮食生产和促进节水的同时，可以更好地平衡区域农业和生态效益。此外，较高的可信度水平对应于较低的系统收益但较大的流域面积。当可信度从 0.6 提高到 0.9 时，系统收益的上限从 13.87 降低 此外，较高的可信度水平对应于较低的系统收益但较大的流域面积。当可信度从 0.6 提高到 0.9 时，系统收益的上限从 13.87 降低 此外，较高的可信度水平对应于较低的系统收益但较大的流域面积。当可信度从 0.6 提高到 0.9 时，系统收益的上限从 13.87 降低$\times {10}^8$元至13.81$\times {10}^8$元而流域面积由原来的41.01 km ²增加到42.12 km ² 。这些不同的最佳结果可以帮助决策者权衡系统收益和违反约束的风险。因此，模型结果可为农作物面积优化提供决策依据，为民勤县及类似研究区的可持续发展提供有价值的依据。