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Numerical solution of fully fuzzy linear systems by fuzzy neural network

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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.

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Acknowledgments

We would like to offer particular thanks to Dr M. A. Rezvani for the editing of this paper. We would also like to thank the referees for valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Islamic Azad University, Firuozkooh Branch, Firuozkooh, Iran

    M. Otadi & M. Mosleh

  2. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, 14778, Iran

    S. Abbasbandy

Authors
  1. M. Otadi
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  2. M. Mosleh
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  3. S. Abbasbandy
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Correspondence to M. Otadi.

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Otadi, M., Mosleh, M. & Abbasbandy, S. Numerical solution of fully fuzzy linear systems by fuzzy neural network. Soft Comput 15, 1513–1522 (2011). https://doi.org/10.1007/s00500-010-0685-9

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