A New Approach to Fuzzy Modeling Using an Extended Kernel Method

Jongcheol KIM; Taewon KIM; Yasuo SUGA

A New Approach to Fuzzy Modeling Using an Extended Kernel Method

Jongcheol KIM, Taewon KIM, Yasuo SUGA

Full Text Views

0

Cite this

Summary :

This paper proposes a new approach to fuzzy inference system for modeling nonlinear systems based on measured input and output data. In the suggested fuzzy inference system, the number of fuzzy rules and parameter values of membership functions are automatically decided by using the extended kernel method. The extended kernel method individually performs linear transformation and kernel mapping. Linear transformation projects input space into linearly transformed input space. Kernel mapping projects linearly transformed input space into high dimensional feature space. Especially, the process of linear transformation is needed in order to solve difficulty determining the type of kernel function which presents the nonlinear mapping in according to nonlinear system. The structure of the proposed fuzzy inference system is equal to a Takagi-Sugeno fuzzy model whose input variables are weighted linear combinations of input variables. In addition, the number of fuzzy rules can be reduced under the condition of optimizing a given criterion by adjusting linear transformation matrix and parameter values of kernel functions using the gradient descent method. Once a structure is selected, coefficients in consequent part are determined by the least square method. Simulated results of the proposed technique are illustrated by examples involving benchmark nonlinear systems.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E86-A No.9 pp.2262-2269

Publication Date: 2003/09/01

Publicized

Online ISSN

DOI

Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)

Category: Neuro, Fuzzy, GA

Cite this

Copy

Jongcheol KIM, Taewon KIM, Yasuo SUGA, "A New Approach to Fuzzy Modeling Using an Extended Kernel Method" in IEICE TRANSACTIONS on Fundamentals, vol. E86-A, no. 9, pp. 2262-2269, September 2003, doi: .
Abstract: This paper proposes a new approach to fuzzy inference system for modeling nonlinear systems based on measured input and output data. In the suggested fuzzy inference system, the number of fuzzy rules and parameter values of membership functions are automatically decided by using the extended kernel method. The extended kernel method individually performs linear transformation and kernel mapping. Linear transformation projects input space into linearly transformed input space. Kernel mapping projects linearly transformed input space into high dimensional feature space. Especially, the process of linear transformation is needed in order to solve difficulty determining the type of kernel function which presents the nonlinear mapping in according to nonlinear system. The structure of the proposed fuzzy inference system is equal to a Takagi-Sugeno fuzzy model whose input variables are weighted linear combinations of input variables. In addition, the number of fuzzy rules can be reduced under the condition of optimizing a given criterion by adjusting linear transformation matrix and parameter values of kernel functions using the gradient descent method. Once a structure is selected, coefficients in consequent part are determined by the least square method. Simulated results of the proposed technique are illustrated by examples involving benchmark nonlinear systems.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e86-a_9_2262/_p

Copy

@ARTICLE{e86-a_9_2262,
author={Jongcheol KIM, Taewon KIM, Yasuo SUGA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A New Approach to Fuzzy Modeling Using an Extended Kernel Method},
year={2003},
volume={E86-A},
number={9},
pages={2262-2269},
abstract={This paper proposes a new approach to fuzzy inference system for modeling nonlinear systems based on measured input and output data. In the suggested fuzzy inference system, the number of fuzzy rules and parameter values of membership functions are automatically decided by using the extended kernel method. The extended kernel method individually performs linear transformation and kernel mapping. Linear transformation projects input space into linearly transformed input space. Kernel mapping projects linearly transformed input space into high dimensional feature space. Especially, the process of linear transformation is needed in order to solve difficulty determining the type of kernel function which presents the nonlinear mapping in according to nonlinear system. The structure of the proposed fuzzy inference system is equal to a Takagi-Sugeno fuzzy model whose input variables are weighted linear combinations of input variables. In addition, the number of fuzzy rules can be reduced under the condition of optimizing a given criterion by adjusting linear transformation matrix and parameter values of kernel functions using the gradient descent method. Once a structure is selected, coefficients in consequent part are determined by the least square method. Simulated results of the proposed technique are illustrated by examples involving benchmark nonlinear systems.},
keywords={},
doi={},
ISSN={},
month={September},}

Copy

TY - JOUR
TI - A New Approach to Fuzzy Modeling Using an Extended Kernel Method
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2262
EP - 2269
AU - Jongcheol KIM
AU - Taewon KIM
AU - Yasuo SUGA
PY - 2003
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E86-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2003
AB - This paper proposes a new approach to fuzzy inference system for modeling nonlinear systems based on measured input and output data. In the suggested fuzzy inference system, the number of fuzzy rules and parameter values of membership functions are automatically decided by using the extended kernel method. The extended kernel method individually performs linear transformation and kernel mapping. Linear transformation projects input space into linearly transformed input space. Kernel mapping projects linearly transformed input space into high dimensional feature space. Especially, the process of linear transformation is needed in order to solve difficulty determining the type of kernel function which presents the nonlinear mapping in according to nonlinear system. The structure of the proposed fuzzy inference system is equal to a Takagi-Sugeno fuzzy model whose input variables are weighted linear combinations of input variables. In addition, the number of fuzzy rules can be reduced under the condition of optimizing a given criterion by adjusting linear transformation matrix and parameter values of kernel functions using the gradient descent method. Once a structure is selected, coefficients in consequent part are determined by the least square method. Simulated results of the proposed technique are illustrated by examples involving benchmark nonlinear systems.
ER -