Re: fuzzy -- in disquise?


Subject: Re: fuzzy -- in disquise?
From: Yaochu Jin (yaochu.jin@hre-ftr.f.rd.honda.co.jp)
Date: Thu Jun 08 2000 - 20:55:22 MET DST


> Dear fuzzyer,

> It is very interesting to bring up this issue again.

>From a mathematic point of view, both fuzzy systems and feedforward NNs are
interpolation algorithms. The basis functions can be triangular, trapzoidal,
Gaussian,
sigmoid, B-splines, wavelets, Fourier series, polynomials and what so ever.
In this sense, all FSs and NNs are roughly the same, which is also obvious.
There also have been a number of papers that show this kind of equivalence
in one way or other.

However, when one calls a systems a FUZZY SYSTEM,
one should be aware that the system should exhibits some fundamental
properties. According to the definition of a fuzzy systems, its variables or
part of
its variables are linguistic variables, which is originated from NATURE
LANGUAGE,
which should be understandable by human being. Thus, one of the most important
features of a FUZZY SYSTEM is its INTERPRETABILITY, or TRANSPARENCY.
With a fuzzy systems at hand, human beings should be able to get some knowledge
about the system that can be expressed by WORDS used by human being in daily
life.

In a word, it might be the high time to emphasize the DIFFERENCE, not the
EQUIVALENCE
between fuzzy systems and FNN. ( It IS acknowledged that for some rigous
analysis
of fuzzy systems, such as stability, universal approximation, it is important to

investigate the mathematic aspects of a fuzzy system.)

For some disccussions on the DIFFERENCES between FS and RBF, please
refer to

Yaochu Jin, W. von Seelen, and B. Senhoff, "Extracting interpretable fuzzy rules
from RBF NNs",
Internal Report, Institut fuer Neuroinformatik, Ruhr-Universitaet Bochum, IR-INI
2000-02, Germany.

> Dear Scientists and Engineers
>
> Unfortunately, fuzzy set theory is nothing
> else but an interpolation algorithm in disguise.
>
> Prof. Dr. Hongxing Li of Beijing Normal
> University has proven it in his paper:
> "Relationship Between Fuzzy Controllers and PID Controllers"
> SCIENCE IN CHINA SERIES E-TECHNOLOGICAL SCIENCES
> 1999, Vol 42, Iss 2, pp 215-224
>
> In fact, he is a fuzzy expert, see
> http://www.crcpress.com/index.htm?catalog/8931
> we must believe his analysis.
>
> You can also write to
> Prof. Hongxing Li
> Dept. of Mathematics
> Beijing Normal University
> Beijing 100875, China
>
> for future discussing
>
> Sincerely yours
> Explore world
>
> ________________________________________________________________________
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>
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--
-------------------------------------------------------------------
Yaochu Jin
Future Technology Research
Honda R&D Europe (D) GmbH
Carl-Legien-Strasse 30
63073 Offenbach/Main
Germany

Tel: +49 69 89011735 Fax: +49 69 89011749 Email: yaochu.jin@hre-ftr.f.rd.honda.jp Alias: yaochu.jin@ieee.org http://www.soft-computing.de/

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