Re: Fundamental questions (long)

Kovalerchuk Boris (borisk@tahoma.cwu.edu)
Fri, 11 Jul 1997 21:01:06 +0200


> Date: Mon, 7 Jul 1997 16:03:46 +0200
> From: Jon Williams <jon@williams-home.demon.co.uk>
> To: Multiple recipients of list <fuzzy-mail@dbai.tuwien.ac.at>
> Subject: Re: Fundamental questions (long)
>
> In article <9707040034.AA00514@sn231.ita.melco.co.jp>, Adrian Cheok
> <cheok@ita.melco.co.jp> writes
> >
> >My first question is what can fuzzy logic do UNIQUELY - i.e that no
> >other method can do. For example you often hear about the application
> >in complex model free systems, and so we can use linguistic knowledge
> >- but what about modeling the system using neural networks or even
> >*conventional* mathematical numerical based models? Under what
> >circumstances will the linguistic knowledge be the ONLY knowledge,
> >and why? Is there ANY theoretical PROOF of the uniqueness of
> >advantage of fuzzy techniques in controlling complex systems?
> >
> None that I am aware of short of a mystical waving of the hands.
>

In [Mouzouris, J. Mendel, 1996] was shown that linguistic information
(rules and membership functions-MFs) is very important in the absence of
sufficient numerical data, but it becomes less important as more
numerical data become available.
Therefore if sufficient numerical data are not available
and there is sufficient trust to linguistic information then it could be
an area, where fuzzy control has the unique advantage.

But this is not the whole story.
If we have a full trust to rules and MFs it is not a justification to use
some particular fuzzy control method, for example, a method based on
minmax and the center of gravity. There are simpler and natural
conventional interpolation ways to use this linguistic information (so
called second interpolation [Kov.,1996, Raimond et al, 1994] at least for
commonly used triangular membership functions.

So there is the UNIQUE area for linguistic information in control
tasks, BUT we can not say the same for particular fuzzy control
methods.

> >Also what is the advantage in using fuzzy logic when it is being
> >trained with numerical data. I don't mean to cause offense but I
> >often read papers that use fuzzy logic trained with numerical data
> >*only* and wonder what was the actual advantage in doing that?
> >
> I suspect fashion and research funding has a lot to do with it, but
> perhaps thats too cynical.
>
> >Lastly but just as importantly, I perceived the main benefit in my
> >application was that the system could cope very well with noisy input
> >data. I have the experimental results to prove it, and I believe it
> >is fundamentally due to the fuzzification of the data, so that noisy
> >data may still trigger the same input sets and thus rules as clean
> >data. However I would like more solid proof of this, does anyone have
> >a reference to a theoretical proof of the ability of fuzzy systems to
> >cope with input noise?
> >
> I think Kosko has tried to prove this but I'm far from convinced.

The length (support) of fuzzy sets (if we trust these sets) can be
considered as an acceptable level of noise.
Mamdani and some other fuzzy controllers differs from conventional
piece-wise interpolation between MFs peak points no more that
10% of MFs support (i.e., noise). So they are practically equivalent for
this situation.
It seems to me that this is one of the explanations of fuzzy control
success.

References:
1. G. Mouzouris, J. Mendel, Designing fuzzy logic systems for uncertain
environments ...In Fuzz-IEEE '96,New Orleans, 1996. v. 1, pp.295-301.
2. B.kovalerchuk, Second interpolation in fuzzy control, In In Fuzz-IEEE
'96,New Orleans, 1996. v. 1, pp.150-155.
3. C.Raimond, S. Boverie, J. Le Quellee, Practical realization of fuzzy
controllers: comparison with conventional methods. In: First European
Congress on fuzzy and intelligent technologies, Aachen, 1993, v. 149-155

Boris Kovalerchuk
---------------
Central Washington University,
Dept. of Comp. Sci.