AUTHOR=Yao Zhao , Li Yingshun 

TITLE=Fuzzy-Weighted Echo State Networks

JOURNAL=Frontiers in Energy Research

VOLUME=Volume 9 - 2021

YEAR=2022

URL=https://www.frontiersin.org/journals/energy-research/articles/10.3389/fenrg.2021.825526

DOI=10.3389/fenrg.2021.825526

ISSN=2296-598X

ABSTRACT=A novel echo state network (ESN), referred to as a fuzzy weighted echo state network (FWESN), is proposed by using the structural information of data sets to improve the performance of the classical ESN.
The information is incorporated into the classical ESN via the concept  of Takagi-Sugeno (TS) models/rules. We employ fuzzy c-mean clustering method to  extract the information based on the given data set.
The antecedent part of TS model is determined by the information. Then,  We obtain new fuzzy rules by replacing the affine models in the consequent part of each TS rule with an classical ESN. Consequently, the output of the proposed FWESN is calculated through inferring these new fuzzy rules by a fuzzy weighted mechanism. The corresponding reservoir is consisted of the sub-reservoirs of the new fuzzy rules. Furthermore, we prove that the FWESN has echo state property by setting the largest spectrum radium of all the internal weight matrices in the sub-reservoirs less than one. Finally,  nonlinear dynamic system  and five nonlinear time series are employed to valid the FWESN.