Simulation and evaluation of fuzzy differential equations by fuzzy neural network

In this paper, a novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented. Here neural network is considered as a part of large field called neural computing or soft computing. The model finds the approximated solution of fuzzy differential equation inside of its domain for the close enough neighborhood of the fuzzy initial point. We propose a learning algorithm from the cost function for adjusting of fuzzy weights. Finally, we illustrate our approach by numerical examples and an application example in engineering.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► An approach for solving the fuzzy differential equations is presented. ► We employ fuzzy neural network for solving fuzzy differential equations. ► We propose a learning algorithm from the cost function for adjusting of weights.