Comparison Between Numerical Solutions of Fuzzy Initial-Value Problems via Interactive and Standard Arithmetics

Abstract

In this work we propose a numerical solution for an n-dimensional initial-value problem where the initial conditions are given by interactive fuzzy numbers. The concept of interactivity is tied to the notion of joint possibility distribution. The numerical solutions are given by the fourth order Runge-Kutta method adapted for the arithmetic operations of interactive fuzzy numbers via sup-J extension, which is a generalization of the Zadeh’s extension principle. We compare this method with the one based on the standard arithmetic. We show that the numerical solutions via interactive arithmetic are contained in the one via standard arithmetic. We provide an application to the SI epidemiological model to illustrate the results.