# Re: Fuzzy Logic & Neural Nets

Pramit 'Jake' Sarma (psarma@che.iitb.ernet.in)
Sat, 11 Dec 1999 17:28:48 +0100 (MET)

Actually, by Weierstrass' Approximation Theorem, a sequence of simple
polynomials can map, or 'handle' any smooth function, on a compact
set. It is also the basis for all the so-called Universal Function Approximator
(UFA) results.

So, then one may ask, if that is so, then why use any of the intelligent
systems mappers when a clearly far simpler set of basis mono/poly-nomials
will do? Why construct a multi-layer neural net (NN), and all of it's
extensions/modifications/enhancements and subject it to
identifications using sophisticated, involved parameter searches?

In the manner of a "step-down" analogy, this is precisely the equivalent
of why's between any two sub-fields in systems: or the
requirement/existence problem is more or less the same for the pair of
(polynomial sequences, neural nets) as for
(neural nets, fuzzy logic). Once begun, this comparison process need not
stop there: fuzzy logic must give way to approximate crisp equation-based
models, in turn to detailed or so-called `truth' equation-based
models, which spirals on, for engineers, into the real physical
system itself ... a 'model' of itself, for the sake of completeness.

Or, the question appears to induce this hierarchy of models - completely
general on one side, to totally specific on the other. But this is
hierarchy is precisely the selection of which produces the meta-field of
'modelling'. Or, perhaps another way of interpreting the question in this
light is "What is the relevance, in modeling, of each of NN and FL"?

It is a question of modelling, related to engineering and systems
practice. It is a question of having a 'toolbox' ... the tools that best
fit a case, are the ones to choose, for efficient handling and good
performance. A "universal wrench" is only sometimes a good answer, and
often not the best. One trades off efficiency for generality. The
important thing is to have this efficiency/generality
information available - from the "domain experts".

On Wed, 8 Dec 1999, Yaochu Jin wrote:

> Hi,
>
> > I hope this question will not offend anyone.
>
> This is a good question.
>
> > Is there anything in fuzzy logic neural nets can't already handle ?
> > RBF, Probabilistic, Kohonen nets and the likes already handle fuzzy
> > classification quite neatly, don;'t they?
>

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Pramit "Jake" Sarma
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