Numerical Solution for Fuzzy Partial Differential Equations with Interactive Fuzzy Boundary Conditions

Abstract

This paper presents a numerical method to solve fuzzy partial differential equations, where the initial and boundary conditions are given by interactive fuzzy numbers. Interactivity is a relationship between fuzzy numbers that is associated with the notion of joint possibility distribution. From this approach, different solutions are presented to the fuzzy partial differential equation. In addition to the method, an algorithm is proposed to determine which of these solutions is most suitable for a given problem. The numerical solution is given by the finite difference method, adapted for the arithmetic operations of interactive fuzzy numbers. The method is applied to the heat equation, in order to illustrate the results.