Multistability of Fuzzy Neural Networks With Rectified Linear Units and State-Dependent Switching Rules

Shiqin Ou; Zhenyuan Guo; Jun Wang

doi:10.1109/TFUZZ.2022.3204895

Multistability of Fuzzy Neural Networks With Rectified Linear Units and State-Dependent Switching Rules

Shiqin Ou, Zhenyuan Guo^*, Jun Wang^*

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

12 Citations (Scopus)

Abstract

This article presents theoretical results on the multistability of fuzzy neural networks with rectified linear units and a state-dependent switching rule. Because of the boundlessness of state activation and multifariousness of state-dependent switching, such fuzzy neural networks exhibit very rich and complex dynamics. We show that there are up to 3ⁿ − 2ⁿ − 1 stable equilibria in an n-neuron switched fuzzy neural network, substantially more than recurrent neural networks without switching. Based on the properties of positive invariant set, we derive seven sets of sufficient conditions to ensure the multistability of switched fuzzy neural networks with rectified linear units. We elaborate on three numerical examples to illustrate the theoretical results and a potential application in associative memories. © 2022 IEEE.

Original language	English
Pages (from-to)	1518-1530
Number of pages	13
Journal	IEEE Transactions on Fuzzy Systems
Volume	31
Issue number	5
Online published	7 Sept 2022
DOIs	https://doi.org/10.1109/TFUZZ.2022.3204895
Publication status	Published - May 2023

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant 62276094, in part by the Natural Science Foundation of Hunan under Grant 2019JJ40022, and in part by the Research Grants Council of Hong Kong Special Administrative Region, under Grant 11202019 and Grant 11203721.

Research Keywords

Biological neural networks
Fuzzy neural network
Fuzzy neural networks
multistability
Neurons
Numerical stability
rectified linear unit (ReLU)
Recurrent neural networks
Stability criteria
state-dependent switching
Switches

RGC Funding Information

RGC-funded

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10.1109/TFUZZ.2022.3204895

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title = "Multistability of Fuzzy Neural Networks With Rectified Linear Units and State-Dependent Switching Rules",

abstract = "This article presents theoretical results on the multistability of fuzzy neural networks with rectified linear units and a state-dependent switching rule. Because of the boundlessness of state activation and multifariousness of state-dependent switching, such fuzzy neural networks exhibit very rich and complex dynamics. We show that there are up to 3n − 2n − 1 stable equilibria in an n-neuron switched fuzzy neural network, substantially more than recurrent neural networks without switching. Based on the properties of positive invariant set, we derive seven sets of sufficient conditions to ensure the multistability of switched fuzzy neural networks with rectified linear units. We elaborate on three numerical examples to illustrate the theoretical results and a potential application in associative memories. {\textcopyright} 2022 IEEE.",

keywords = "Biological neural networks, Fuzzy neural network, Fuzzy neural networks, multistability, Neurons, Numerical stability, rectified linear unit (ReLU), Recurrent neural networks, Stability criteria, state-dependent switching, Switches",

author = "Shiqin Ou and Zhenyuan Guo and Jun Wang",

year = "2023",

month = may,

doi = "10.1109/TFUZZ.2022.3204895",

language = "English",

volume = "31",

pages = "1518--1530",

journal = "IEEE Transactions on Fuzzy Systems",

issn = "1063-6706",

publisher = "IEEE",

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TY - JOUR

T1 - Multistability of Fuzzy Neural Networks With Rectified Linear Units and State-Dependent Switching Rules

AU - Ou, Shiqin

AU - Guo, Zhenyuan

AU - Wang, Jun

PY - 2023/5

Y1 - 2023/5

N2 - This article presents theoretical results on the multistability of fuzzy neural networks with rectified linear units and a state-dependent switching rule. Because of the boundlessness of state activation and multifariousness of state-dependent switching, such fuzzy neural networks exhibit very rich and complex dynamics. We show that there are up to 3n − 2n − 1 stable equilibria in an n-neuron switched fuzzy neural network, substantially more than recurrent neural networks without switching. Based on the properties of positive invariant set, we derive seven sets of sufficient conditions to ensure the multistability of switched fuzzy neural networks with rectified linear units. We elaborate on three numerical examples to illustrate the theoretical results and a potential application in associative memories. © 2022 IEEE.

AB - This article presents theoretical results on the multistability of fuzzy neural networks with rectified linear units and a state-dependent switching rule. Because of the boundlessness of state activation and multifariousness of state-dependent switching, such fuzzy neural networks exhibit very rich and complex dynamics. We show that there are up to 3n − 2n − 1 stable equilibria in an n-neuron switched fuzzy neural network, substantially more than recurrent neural networks without switching. Based on the properties of positive invariant set, we derive seven sets of sufficient conditions to ensure the multistability of switched fuzzy neural networks with rectified linear units. We elaborate on three numerical examples to illustrate the theoretical results and a potential application in associative memories. © 2022 IEEE.

KW - Biological neural networks

KW - Fuzzy neural network

KW - Fuzzy neural networks

KW - multistability

KW - Neurons

KW - Numerical stability

KW - rectified linear unit (ReLU)

KW - Recurrent neural networks

KW - Stability criteria

KW - state-dependent switching

KW - Switches

UR - http://www.scopus.com/inward/record.url?scp=85137892264&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85137892264&origin=recordpage

U2 - 10.1109/TFUZZ.2022.3204895

DO - 10.1109/TFUZZ.2022.3204895

M3 - RGC 21 - Publication in refereed journal

SN - 1063-6706

VL - 31

SP - 1518

EP - 1530

JO - IEEE Transactions on Fuzzy Systems

JF - IEEE Transactions on Fuzzy Systems

IS - 5

ER -

Multistability of Fuzzy Neural Networks With Rectified Linear Units and State-Dependent Switching Rules

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Multistability of Fuzzy Neural Networks With Rectified Linear Units and State-Dependent Switching Rules

Abstract

Funding

Research Keywords

RGC Funding Information

Access Output

Other Access Options

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GRF: Neurodynamics-driven Optimization and Control of Intelligent Heating, Ventilation and Air Conditioning Systems

GRF: Collaborative Neurodynamic Approaches to Portfolio Optimization

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