Comparison of two approaches for solving a fuzzy system describing the degradation kinetics of pesticides in plant uptake models

\nChemical control in agriculture includes the use of chemical agents whose concentrations in the harvest products decrease over time. We analyze mathematically the decrease of pesticide residues in potato tubers, and estimate the involved parameters to predict the evolution of pesticide residual after the last spraying. First, we propose and solve a fuzzy initial value problem (FIVP) associated with a fuzzy differential equations system modeling the pesticide concentration in potato tubers. Second, we apply our model in a real situation, where the evolution of the concentration of chemicals is required, by considering two approaches. In the first one, based on a small set of field data, we use a polynomial regression (LOESS) to input new data and estimate the parameters involved in the FIVP and thus, we determinate the evolution of the concentration of the thiamethoxam, a pesticide used on potato crops. In the second approach, we design a Takagi–Sugeno–Kang model to approximate the degradation of thiamethoxam concentration, by defining a set of fuzzy inference rules based on the data provided by LOESS regression. These two approaches show a similar and good behavior, even having few fuzzy data. Our analysis can be applied in a large class of dynamical systems.\n