Jafari, R orcid.org/0000-0001-7298-2363, Yu, W, Li, X et al. (1 more author) (2017) Numerical Solution of Fuzzy Differential Equations with Z-numbers Using Bernstein Neural Networks. International Journal of Computational Intelligence Systems, 10 (1). pp. 1226-1237. ISSN 1875-6891
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/). |
Keywords: | Fuzzy differential equations, Bernstein neural networks, Z- numbers, Uncertain nonlinear systems |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Arts, Humanities and Cultures (Leeds) > School of Design (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 28 Jan 2020 15:04 |
Last Modified: | 25 Jun 2023 22:08 |
Status: | Published |
Publisher: | Atlantis Press |
Identification Number: | 10.2991/ijcis.10.1.81 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:156079 |