Modeling approach for the parameters of von Bertalanffy growth equation

The von Bertalanffy growth equation is among the most widely used mathematical tool for modeling the growth curve of animal mass as a function of time. The main parameters of the model are the rates of anabolism and catabolism which are estimated under various approaches. These parameters are explored in this study, apply to a data set collected by a research on Zebu cattle breed. The goal of this study is building a mathematical model that interprets the dynamic of the mass in function of time for the collected data. With that aim, it has been theoretically proved that, corresponding to an intervals of values for the parameters in certain order, the curve solutions of the equation are as well ordered in a continuous range. Computationally, this range is determined from an estimate of the parameters of the von Bertalanffy equation through Levenberg–Marquardt method. To finalize the mathematical interpretation of the data, an interval type-2 fuzzy set is logically built from a query made to the experts in the matter.