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On Mar 1, 2:06 am, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
> > As I understand it, fuzzy logic as a whole can be grounded in fuzzy
> > set theory. That in case is founded in real membership functions in
> > orthodox sets.
>
> If "by real membership functions" you mean that the fuzzy membership is
> the same the classical membership, then you are wrong.
By "real" I meant "real valued". Because of that, there's nothing in fuzzy set theory you couldn't handle with rather boring and classical measure theoretic tools.
> >The theory of real functions, measures and the like is then
> > formulated on top of normal ZFC axiomatics.
>
> They cannot be so formulated, because the fuzzy set membership is
> different from the the classical set membership and reducible only in
> the trivial case of the fuzzy membership coinciding with the classical
> membership.
That's not what I was arguing for. Of course a fuzzy set is different from a classical one. But this still doesn't change the fact that at the bottom, it's defined in terms of classical logic, set theory and measures. We have an extra layer of indirection, yes, but it adds little interesting to the overall picture. Received on Thu Mar 01 2007 - 01:18:44 CST