Re: 1 NF

From: V.J. Kumar <vjkmail_at_gmail.com>
Date: Thu, 1 Mar 2007 19:17:08 +0100 (CET)
Message-ID: <Xns98E68726C80C7vdghher@194.177.96.26>

"Sampo Syreeni" <decoy_at_iki.fi> wrote in news:1172733524.671700.195990 @k78g2000cwa.googlegroups.com:

> 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.

Are you saying that the membership function is just another name for the classical measure ?

>> >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.

How would you define a degree of truth in classical logic without resorting to any additonal tools which would be cheating ?

How would you define the membership function as measure ?

> We have an extra layer of indirection, yes, but it adds
> little interesting to the overall picture.
>
>
Received on Thu Mar 01 2007 - 12:17:08 CST