Solving linear Fredholm fuzzy integral equations of the second kind by artificial neural networks

Abstract

This paper deals with the solutions of fuzzy Fredholm integral equations using neural networks. Based on the parametric form of a fuzzy number, a Fredholm fuzzy integral equation converts to two systems of integral equations of the second kind in the crisp case. This method employs a growing neural network as the approximate solution of the integral equations, for which the activation functions are log-sigmoid and linear functions. The parameters of the approximate solution are adjusted by using an unconstrained optimization problem. In order to show this capability and robustness, some fuzzy Fredholm integral equations are solved in detail as numerical examples.

Keywords

• Fuzzy numbers
• Fredholm fuzzy integral equations
• Artificial neural networks