Numerical Solution of Fuzzy Differential Equations with Z-numbers Using Bernstein Neural Networks

DOI

10.2991/ijcis.10.1.81How to use a DOI?

Keywords

Fuzzy differential equations; Bernstein neural networks; Z- numbers; Uncertain nonlinear systems

Abstract

The uncertain nonlinear systems can be modeled with fuzzy equations or fuzzy differential equations (FDEs) by incorporating the fuzzy set theory. The solutions of them are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs.

In this paper, the solutions of FDEs are approximated by two types of Bernstein neural networks. Here, the uncertainties are in the sense of Z-numbers. Initially the FDE is transformed into four ordinary differential equations (ODEs) with Hukuhara differentiability. Then neural models are constructed with the structure of ODEs. With modified back propagation method for Z-number variables, the neural networks are trained. The theory analysis and simulation results show that these new models, Bernstein neural networks, are effective to estimate the solutions of FDEs based on Z-numbers.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

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TY  - JOUR
AU  - Raheleh Jafari
AU  - Wen Yu
AU  - Xiaoou Li
AU  - Sina Razvarz
PY  - 2017
DA  - 2017/09/19
TI  - Numerical Solution of Fuzzy Differential Equations with Z-numbers Using Bernstein Neural Networks
JO  - International Journal of Computational Intelligence Systems
SP  - 1226
EP  - 1237
VL  - 10
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.10.1.81
DO  - 10.2991/ijcis.10.1.81
ID  - Jafari2017
ER  -