An interactive inexact fuzzy bounded programming approach for agricultural water quality management

•An interactive inexact fuzzy bounded programming method is developed.•It can tackle the conflict between maximizing the objective and meeting constraints.•A case study is applied to illustrate applicability of the proposed method.•The final decisions are with conflicting aspiration levels and violation risk.•Results can help identify optimal agricultural water quality management schemes. An interactive inexact fuzzy bounded programming (IFBP) approach is developed through introducing the concept of fuzzy bounded intervals into an interactive fuzzy compromise programming framework. It can provide decision support for decision makers with conflicting desires of greater objective value and higher safety levels of constraints. In this model, by determining a fuzzy goal associated with different feasibility degrees from a semantic correspondence, the degrees of satisfying each objective can be calculated. Decision makers can intervene in every step of the decision process through analyzing the degrees of approaching the aspiration levels and the risks of violating the constraints. The developed method is applied to an agricultural water quality management case for optimizing planting area, manure/fertilizer application amount, and livestock husbandry size. Results indicated that an increased feasibility degree would correspond to a reduced system benefit. Generally, by analyzing risks of violating the constraints in all solution processes, decision makers who have their own aspiration levels would be able to obtain a balanced solution considering the conflict between satisfying the aspiration levels and minimizing the violation risks.