Abstract
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 13.87×108 Yuan to 13.81×108 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.
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