Fuzzy differential equation with completely correlated parameters

In this paper we study fuzzy differential equations with parameters and initial conditions interactive. The interactivity is given by means of the concept of completely correlated fuzzy numbers. We consider the problem in two different ways: the first by using a family of differential inclusions; in the second the extension principle for completely correlated fuzzy numbers is employed to obtain the solution of the model. We conclude that the solutions of the fuzzy differential equations obtained by these two approaches are the same. The solutions are illustrated with the radioactive decay model where the initial condition and the decay rate are completely correlated fuzzy numbers. We also present an extension principle for completely correlated fuzzy numbers and we show that Nguyen's theorem remains valid in this environment. In addition, we compare the solution via extension principle of the fuzzy differential equation when the parameters are non-interactive fuzzy numbers and when the parameters are completely correlated fuzzy numbers. Finally, we study the SI-epidemiological model in two forms: first considering that the susceptible and infected individuals are completely correlated and then assuming that the transfer rate and the initial conditions are completely correlated.