An analytical method for solving linear Fredholm fuzzy integral equations of the second kind

In this paper, we use the parametric form of a fuzzy number and convert a linear fuzzy Fredholm integral equation to two linear systems of integral equations of the second kind in the crisp case. For fuzzy Fredholm integral equations with kernels, the sign of which is difficult to determine, a new parametric form of the fuzzy Fredholm integral equation is introduced. We use the homotopy analysis method to find the approximate solution of the system, and hence, obtain an approximation for fuzzy solutions of the linear fuzzy Fredholm integral equation of the second kind. The proposed method is illustrated by solving some examples. Using the HAM, it is possible to find the exact solution or the approximate solution of the problem in the form of a series.