Re: fuzzy -- in disquise?

Subject: Re: fuzzy -- in disquise?
From: Javier (McQues) Gomez Marin-Blazquez (
Date: Sat Jun 10 2000 - 07:16:51 MET DST

Yaochu pointed to one of the, IMHO, on of the most useful features of
applying Fuzzy Logic: INTERPRETABILITY.

One may easily fall into the belief that all the fuzzy systems around
are approximatives (by approximative one understands fuzzy systems where
the concern is in the accuracy only and so the linguistic variables
associated with the fuzzy sets are either inexistant or so disrupted by
data-driven-only tuning algorithms that they have lost the original
meaning). But there exists other kind of fuzzy rule systems, the
descriptive ones, where the linguistic interpretation is the most
important point. Here, the human-defined sets (the humans provide the
sets and its interpretation, that is, they provide the "words" the rule
system will use) are not modified and the rules obtained shows the
behaviour of the system modelled (or at least is a model that shows the
behaviour, one can not say that is the real system, but it may be
considered equivalent). There are efforts to create highly-accurate and
at the same time interpretable rule systems that overcome the fixed-grid
problem. For results in this line one can consult (I hate
self-referencing but this is the purest descriptive line I am aware of.
I'll be glad if someone are aware of more and point them to me):

J. G. Marin-Blazquez, Q. Shen , A. F. Gómez Skarmeta
"From Approximative to Descriptive Models", In Proceedings of the
9th IEEE International Conference on Fuzzy Systems, Fuzz-IEEE 2000
San Antonio, Texas, USA, May 2000.

Other line to reach interpretability through set reduction (the system
give the words to be used, but the number is low enough and the sets are
different enough to allow humans post-assign a linguistic label) is
being researched by:

M. Setnes and R. Babuska and H. B. Verbruggen
"Transparent Fuzzy Modelling"
International Journal of Human-Computer Studies Vol 49, Number 2, pag.
159-179, 1998

Roubos J.A., Setnes M. "Compact fuzzy models through complexity
reduction and evolutionary optimization"
Fuzz-IEEE 2000 Trans., pp 762-767,

Desirable features to reach a clear interpretability can be found in:

Valente de Oliveira J. (1999)
Semantic constrains for memberships function optimization. IEEE Trans.
FS 128-138.

In the bibliography of them can be found more information.

I believe that a Fuzzy Rule System is more than just an interpolator...
it gives a great deal of information about the system behaviour that is
much more than just give predictions.

NN can be equivalent, but they give no clue about "why". But Descriptive
Fuzzy Rule Systems, fortunately, does.

Javier G. Marin-Blazquez
PhD Student
School of AI
The University of Edinburgh
Scotland, UK, EU.

Yaochu Jin wrote:
> > 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
> which should be understandable by human being. Thus, one of the most important
> 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
> 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.

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