Simulation and evaluation of second order fuzzy boundary value problems
In a conventional approach to numerical computation, finite difference and finite element methods are usually implemented to determine the fuzzy solution of a set of fuzzy differential equations (FDEs) This paper presents a novel approach to solve FDEs by applying the universal approximations method through an artificial intelligence utility in a simple way. In this proposed method, fuzzy neural networks (FNNs) are applied as universal approximators for FDEs. Fuzzy neural network can be trained with crisp and fuzzy data. In this paper, a novel hybrid method based on FNN for the solution of second order differential equations with fuzzy boundary conditions is presented. We propose a learning algorithm from the cost function to adjust fuzzy weights. Finally, I illustrate my approach with some numerical examples and at the same time one example in engineering is designed.
Soft Comput.