Objective The conventional unary quadratic polynomial model (QPRM) and unary non-structural fertilizer response model (UNRM) were improved by a unary grey model (GM) for fertilization optimization at vegetable farms.

Method According to the grey Verhulst model within the framework of grey system theory, 28 field experiments were conducted using an ascending rate of NPK fertilization on a vegetable yield. Fitting the corresponding vegetable yields of the lots in the models was used to determine their prediction reliabilities.

Result An S-shaped function between fertilizer application and vegetable yield with GM on 25 of the experiments was statistically significant. Either positive or negative coefficients of the models conformed to the general laws with the recommended fertilization rates fell within the designed range. They were of typical fertilizer response type displaying a success rate of 89.3%, which was 1.8 times and 1.4 times higher than those applied QPRM and UNRM, respectively. The models from the remaining three experiments that failed statistical significance test belonged to the non-typical type. The GM recommended fertilizer application rate fluctuated at the range of R = −1 to R = −0.6 but stabilized as R increased beyond −0.6. The optimal R for N application was −0.6, and 0 for P and K. Although the fertilization recommended by GM, as well as the other two models, significantly correlated linearly with the maximum and economic application rates (P＜0.01), it was 82.5% and 83.5% on N, 106.6% and 114.1% on P, and 107.6% and 108.9% on K of what were suggested by QPRM and UNRM, respectively.

Conclusion The vegetable field experimentation significantly verified the high fitting between the fertilizer application and vegetable yield and the significantly improved accuracy of GM over the previously used models.