Numerical solutions for bidimensional initial value problem with interactive fuzzy numbers

Abstract

We present a comparison between two approaches of numerical solutions for bidimensional initial value problem with interactive fuzzy numbers. Specifically, we focus on SI epidemiological model considering that initial conditions are given by interactive fuzzy numbers. The interactivity is based on the concept of joint possibility distribution and for this model, it is possible to observe two types of interactivities for fuzzy numbers. The first one is based on the completely correlated concept, while the other one is given by a family of joint possibility distributions. The numerical solutions are given using Euler’s method adapted for the arithmetic operations of interactive fuzzy numbers via sup-J extension principle, which generalizes the Zadeh’s extension principle.