Re: Adaptative fuzzy systems and classification

david_olmsted@my-dejanews.com
Tue, 22 Sep 1998 02:52:47 +0200 (MET DST)

In article <19980918120132.23531.00001032@ng127.aol.com>,
earlcox@aol.com (EarlCox) wrote:
>
> I'll let my friend Bill Siler answer most of this, but I fail to see how JL's
> logic is a superset of fuzzy logic. Fuzzy logic is, of course, an infinitely
> valued logic. It has more general and broader operations than Lukasiewicz's
> logic. And, of course, thousands of products and decisions models have been
> built using fuzzy logic (not that this means anything from an "strength of
> axioms" viewpoint, but it should give us a reason to explore the mechanics of
> fuzzy logic in some detail.).
>
> Fuzzy logic has been used extensively in adaptive neural networks in a broad
> spectrum of applications including general pattern recognition, fault
> detection, comercial loan analysis, portfolio balancing and safety, and so
> forth. I've used an adaptive Kohonen network coupled with fuzzy logic in
> medicare fraud detection. I wrote an article five years ago in AI Expert
> magazine on Fuzzy Neural Networks showing how fuzzy logic could be used as
> operators and how fuzzy thresholds improve the classification capabilities of
> neural networks.
>
> Anyway, the bottom line is this: I'm not sure what distinction you are making
> between "your" multivalued logic and the fuzzy logic used by the rest of the
> working universe.
>
> Earl
>
Hi Earl,

My main point is that Fuzzy Set Theory as originally formulated by Zadeh and
later called fuzzy logic does not have a definition for the IMPLICATION
operation or its negated form the CONDITIONAL operation (equivalent to
mathematical subraction). Since fuzzy logic missing these operations it does
not have as many operations as the Multivalued Logic formulated by
Lukasiewicz. Consequently fuzzy logic is a subset of multivalued logic since
the other operations are equivalent. For more information on the relation
between the two see my web site at http://www.neurocomputing.org.

I happen to have some of your AI Expert articles in my files and yes you can
couple fuzzy set theory with neural network theory since both use analog
values. The inputs to neural networks can be fuzzy set membership values. The
key word is couple. As I have shown at my web site one can MAKE a two stage
neural network with multivalued logic operations with the first stage using a
strategy similar to that used in the ART network of Stephen Grossburg (but
simpler, more flexible, and more robust.)

One can also replace the adaptive weights in some neural networks with fuzzy
set definers are you did in your article "Integrating Fuzzy Logic into Neural
Nets" but that does not involve the operations of the network which are used
to combine the line signals.

Sincerely,
David Olmsted

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