An interval nonlinear multiobjective programming model with fuzzy-interval credibility constraint for crop monthly water allocation

Nonlinear and conflicting objectives as well as complex uncertainties are commonly encountered by irrigation-water managers. To address such problems, an interval nonlinear multiobjective programming model with fuzzy-interval credibility constraint (FIC-INMP) is proposed for crop water allocation. The FIC-INMP model integrating interval programming, nonlinear multiobjective programming and fuzzy-interval credibility-constrained programming could address not only the conflicts of multiple nonlinear objectives under interval uncertainty, but also the fuzziness expressed as fuzzy-interval membership function. Moreover, an interval fuzzy weighted (IFW) method is proposed to solve developed model by integrating fuzzy weighted programming approach and interval Zimmermann fuzzy method. The FIC-INMP and IFW are applied to Yingke Irrigation District to plan crop monthly water allocation and demonstrate their applicability. By fully considering the main factors in allocation, including concerns of different decision makers, normal growth of crops, local water balance and uncertainties existing in allocation, optimal crop water-allocation schemes can be obtained via the FIC-INMP and IFW. The optimal results offer abundant schemes to decision makers by trading off benefit and risk. In addition, from the comparison between single objective and multiobjective model, the multiobjective model shows better practicality due to more reasonable water allocation in critical water demand period of crops. These results can effectively contribute to the local irrigation water management and ecological restoration.