Fuzzy multi-objective linear programming applying to crop area planning

Crop area planning plays significant role in agricultural water management. During the planning, because of ambiguous or uncertain information caused by the vagueness of decision makers’ subjective preference or the uncertainty of objective information, conventional multi-objective linear programming (MOLP) model is not suitable for such decision-making in such fuzzy environment. In this study, we proposed the fuzzy multi-objective linear programming (FMOLP) model with triangular fuzzy numbers and transformed the FMOLP model and its corresponding fuzzy goal programming (FGP) problem to crisp ones which can be solved by the conventional programming methods. The FMOLP model was applied to crop area planning of Liang Zhou region, Gansu province of northwest China, and then the optimal cropping patterns under different water-saving levels and satisfaction grades for water resources availability of the decision makers (DM) were obtained. Compared to the MOLP model, the FMOLP model itself expresses the fuzzy information effectively, and its solutions can represent the DMs satisfactory degree of the subjective preference and propose alternative solutions for better decision support when applied in the crop area planning.