Simulation and evaluation of system of fuzzy linear Fredholm integro-differential equations with fuzzy neural network

Abstract

In this paper, fuzzy neural network (FNN) can be trained with crisp and fuzzy data. The work of this paper is an expansion of the research of fuzzy linear Fredholm integro-differential equations. In this work, we interpret a fuzzy integro-differential equations. In this paper, a novel hybrid method based on FNN and Newton–Cotes methods with positive coefficient for the solution of system of fuzzy linear Fredholm integro-differential equations of the second kind with fuzzy initial values is presented. The problem formulation of the proposed UA is quite straightforward. To obtain the “best-approximated” solution of system of fuzzy linear Fredholm integro-differential equations, the adjustable parameters of PFNN are systematically adjusted by using the learning algorithm. Within this paper, the fuzzy neural network model is used to obtain an estimate for the fuzzy parameters in a statistical sense. Based on the extension principle, a simple algorithm from the cost function of the fuzzy neural network is proposed, in order to find the approximate parameters. We propose a learning algorithm from the cost function for adjusting of fuzzy weights. Here neural network is considered as a part of a larger field called neural computing or soft computing. Finally, we illustrate our approach by some numerical examples.