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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