Fuzzy Calculus by RBF Neural Networks

Zhenquan Li; Vojislav Kecman

Fuzzy Calculus by RBF Neural Networks

Zhenquan Li, Vojislav Kecman

University of Auckland

Research output: Book chapter/Published conference paper › Chapter (peer-reviewed) › peer-review

Abstract

The paper presents novel modeling of fuzzy inference system by using the ‘fuzzified’ radial basis function (RBF) neural network (NN). RBF NN performs the mapping of the antecedent fuzzy numbers (a.k.a. membership functions, attributes, possibilities degrees) into the consequent ones. In this way, an RBF NN is capable of performing the rigorous calculus with fuzzy numbers. Prior the mapping, both the antecedents and the consequents are discretized and transferred into the n-dimensional and m-dimensional ‘fuzzy’ vectors. These vectors present the training inputs and outputs of an RBF NN and, in this way, an RBF network performs an exact R n → R m mapping. The generalization capacity of such a neural implementation is superior to the ability of the original fuzzy model.

Original language	English
Title of host publication	Advances in soft computing
Subtitle of host publication	Neural Networks and Soft Computing
Editors	Leszek Rutkowski, Jaunsz Kacprzyk
Publisher	Springer Heidelberg
Chapter	Advances in Soft Computing book series, Vol. 19
Pages	516-522
Volume	19
ISBN (Electronic)	978-3-7908-1902-1
ISBN (Print)	978-3-7908-0005-0
Publication status	Published - 2003

Access to Document

https://link.springer.com/chapter/10.1007%2F978-3-7908-1902-1_79

Mathematical and Compuational Applications (Journal)
Li, Z. (Reviewer)
01 Sept 2023 → 30 Oct 2023
Activity: Publication peer-review and editorial work › Peer review responsibility, including review panel or committee

Cite this

@inbook{0110c0258b854302b20340e14706ae11,

title = "Fuzzy Calculus by RBF Neural Networks",

abstract = "The paper presents novel modeling of fuzzy inference system by using the {\textquoteleft}fuzzified{\textquoteright} radial basis function (RBF) neural network (NN). RBF NN performs the mapping of the antecedent fuzzy numbers (a.k.a. membership functions, attributes, possibilities degrees) into the consequent ones. In this way, an RBF NN is capable of performing the rigorous calculus with fuzzy numbers. Prior the mapping, both the antecedents and the consequents are discretized and transferred into the n-dimensional and m-dimensional {\textquoteleft}fuzzy{\textquoteright} vectors. These vectors present the training inputs and outputs of an RBF NN and, in this way, an RBF network performs an exact R n → R m mapping. The generalization capacity of such a neural implementation is superior to the ability of the original fuzzy model.",

keywords = "membership function, Radial basis function, fuzzy number, fuzzy model, inference rule",

author = "Zhenquan Li and Vojislav Kecman",

year = "2003",

language = "English",

isbn = "978-3-7908-0005-0",

volume = "19",

pages = "516--522",

editor = "Leszek Rutkowski and Jaunsz Kacprzyk",

booktitle = "Advances in soft computing",

publisher = "Springer Heidelberg",

address = "Germany",

}

TY - CHAP

T1 - Fuzzy Calculus by RBF Neural Networks

AU - Li, Zhenquan

AU - Kecman, Vojislav

PY - 2003

Y1 - 2003

N2 - The paper presents novel modeling of fuzzy inference system by using the ‘fuzzified’ radial basis function (RBF) neural network (NN). RBF NN performs the mapping of the antecedent fuzzy numbers (a.k.a. membership functions, attributes, possibilities degrees) into the consequent ones. In this way, an RBF NN is capable of performing the rigorous calculus with fuzzy numbers. Prior the mapping, both the antecedents and the consequents are discretized and transferred into the n-dimensional and m-dimensional ‘fuzzy’ vectors. These vectors present the training inputs and outputs of an RBF NN and, in this way, an RBF network performs an exact R n → R m mapping. The generalization capacity of such a neural implementation is superior to the ability of the original fuzzy model.

AB - The paper presents novel modeling of fuzzy inference system by using the ‘fuzzified’ radial basis function (RBF) neural network (NN). RBF NN performs the mapping of the antecedent fuzzy numbers (a.k.a. membership functions, attributes, possibilities degrees) into the consequent ones. In this way, an RBF NN is capable of performing the rigorous calculus with fuzzy numbers. Prior the mapping, both the antecedents and the consequents are discretized and transferred into the n-dimensional and m-dimensional ‘fuzzy’ vectors. These vectors present the training inputs and outputs of an RBF NN and, in this way, an RBF network performs an exact R n → R m mapping. The generalization capacity of such a neural implementation is superior to the ability of the original fuzzy model.

KW - membership function

KW - Radial basis function

KW - fuzzy number

KW - fuzzy model

KW - inference rule

M3 - Chapter (peer-reviewed)

SN - 978-3-7908-0005-0

VL - 19

SP - 516

EP - 522

BT - Advances in soft computing

A2 - Rutkowski, Leszek

A2 - Kacprzyk, Jaunsz

PB - Springer Heidelberg

ER -

Fuzzy Calculus by RBF Neural Networks

Abstract

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Mathematical and Compuational Applications (Journal)

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