Numerical solution of fuzzy linear Fredholm integro-differential equation by \\fuzzy neural network

In this paper, a novel hybrid method based on learning algorithm of fuzzy neural network and Newton-Cotes methods with positive coefficient for the solution of linear Fredholm integro-differential equation of the second kind with fuzzy initial value is presented. Here neural network is considered as a part of large field called neural computing or soft computing. We propose a learning algorithm from the cost function for adjusting fuzzy weights. This paper is one of the first attempts to derive learning algorithms from fuzzy neural networks with real input, fuzzy output, and fuzzy weights. Finally, we illustrate our approach by numerical examples.