Numerical solution of fully fuzzy linear systems by fuzzy neural network

Abstract

In this paper, a new hybrid method based on fuzzy neural network (FNN) for approximate solution of fuzzy linear systems of the form $$Ax=d,$$ where $$A$$ is a square matrix of fuzzy coefficients, $$x$$ and $$d$$ are fuzzy number vectors, is presented. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate solution of an $$n\times n$$ system of fuzzy linear equations that supposedly has a unique fuzzy solution, a simple algorithm from the cost function of the FNN is proposed. Finally, we illustrate our approach by some numerical examples.