Finite Difference Method for Intuitionistic Fuzzy Partial Differential Equations

Abstract

In this paper, we investigate an intuitionistic fuzzy Poisson equation with uncertain parameters, considering the parameters as intuitionistic fuzzy numbers. We apply a finite difference method to solve the ‘Intuitionistic fuzzy Poisson equation’. The continuity of the membership and non-membership functions (which imply the continuity of the hesitancy function) is used to obtain qualitative properties on regular α-cut and β-cut of the intuitionistic fuzzy solution. The fuzzification of the deterministic α-cut and β-cut solutions obtained lead to the intuitionistic fuzzy solution. Finally, an example is presented to illustrate the proposed methodology, as well as to show a graphical representation of its corresponding intuitionistic fuzzy solution.

Keywords

• intuitionistic fuzzy number
• fuzzy Poisson equation
• finite difference scheme