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Stability of Evolving Fuzzy Systems Based on Data Clouds

Rong, Hai-Jun, Angelov, Plamen P., Gu, Xiaowei, Bai, Jian-Ming (2018) Stability of Evolving Fuzzy Systems Based on Data Clouds. IEEE Transactions on Fuzzy Systems, 26 (5). pp. 2774-2784. ISSN 1063-6706. (doi:10.1109/TFUZZ.2018.2793258) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:90401)

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Evolving fuzzy systems (EFSs) are now well developed and widely used, thanks to their ability to self-adapt both their structures and parameters online. Since the concept was first introduced two decades ago, many different types of EFSs have been successfully implemented. However, there are only very few works considering the stability of the EFSs, and these studies were limited to certain types of membership functions with specifically predefined parameters, which largely increases the complexity of the learning process. At the same time, stability analysis is of paramount importance for control applications and provides the theoretical guarantees for the convergence of the learning algorithms. In this paper, we introduce the stability proof of a class of EFSs based on data clouds, which are grounded at the AnYa type fuzzy systems and the recently introduced empirical data analytics (EDA) methodological framework. By employing data clouds, the class of EFSs of AnYa type considered in this paper avoids the traditional way of defining membership functions for each input variable in an explicit manner and its learning process is entirely data driven. The stability of the considered EFS of AnYa type is proven through the Lyapunov theory, and the proof of stability shows that the average identification error converges to a small neighborhood of zero. Although, the stability proof presented in this paper is specially elaborated for the considered EFS, it is also applicable to general EFSs. The proposed method is illustrated with Box-Jenkins gas furnace problem, one nonlinear system identification problem, Mackey-Glass time series prediction problem, eight real-world benchmark regression problems as well as a high-frequency trading prediction problem. Compared with other EFSs, the numerical examples show that the considered EFS in this paper provides guaranteed stability as well as a better approximation accuracy.

Item Type: Article
DOI/Identification number: 10.1109/TFUZZ.2018.2793258
Uncontrolled keywords: Fuzzy systems; Stability criteria; Numerical stability; Algorithm design and analysis; Adaptation models; Training; AnYa type fuzzy systems; data clouds; evolving fuzzy systems (EFSs); stability
Subjects: Q Science > QA Mathematics (inc Computing science) > QA 75 Electronic computers. Computer science
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Computing
Depositing User: Amy Boaler
Date Deposited: 28 Sep 2021 10:03 UTC
Last Modified: 29 Sep 2021 11:26 UTC
Resource URI: (The current URI for this page, for reference purposes)
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