ABSTRACT In order to estimate the response of biometric variables in different irrigation depths in radish crop, as well as their relations in the development of the crop, a fuzzy mathematical analysis was carried out from irrigation with depths of different percentages of the crop evapotranspiration (ETc), using Gaussian pertinence functions for the input variable and triangular for the biometric output variables. Validations were performed using neural network models, smoothing splines and polynomial regression. The relation among the biometric variables was measured applying the Pearson correlation coefficient. The results showed that the fuzzy modeling presented superiority in the crop development estimate over the quadratic polynomial regression model, neural network and smoothing splines, because it achieved an average reduction of errors among the biometric variables, of 7.8% 94.6% and 9.2% for the RMSE in the respective models, as well as a better adjustment of the data with average R2 of the variables. The modeling with neural network showed inadequate agronomic behavior in data representation. Regarding biometric variables, the length and diameter of the tuberous root are inversely correlated, and the fresh phytomass of the tuberous root is correlated only with the fresh phytomass of the root.

ABSTRACT The productivity of a crop is related to the water demand inserted in its development. The measurement of water and its optimization directly influences the final costs of crop production for agricultural producers. In this sense, the objective of this study is evaluating the fuzzy modeling in estimating the productivity of the radish crop (fresh phytomass of the tuberous root) affected by different irrigation depths (25%, 50%, 75%, 100%, and 125%), based on evapotranspiration of the crop (ETc). To measure the results, two fuzzy systems (with triangular and Gaussian membership functions respectively) and a polynomial regression model were developed to perform model validation comparisons. The fuzzy modeling showed a better fit of the data compared to the polynomial regression model, with reduced errors (RMSE with values 6.3 and 6.9 in the fuzzy models versus 8.8 in the regression model) and higher correlation coefficient (0.54 and 0.5 fuzzy versus 0.1 regression). The triangular fuzzy model estimated the best crop yield (31.9 g of fresh phytomass) when using a 100% ETc depth. Also, the curve generated by the fuzzy model accurately represents all the productivity averages in each depth, in addition to this model presenting the smallest errors (compared to the triangular model and the regression model) and the highest R2. However, the Gaussian fuzzy model proved to be more efficient in representing the agronomic reality, as it does not have peaks and valleys, and it is a smooth model in both growth and degrowth.