SUO: Re: Plea for Relements
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[Reposted after 10 hrs]
John F. Sowa wrote:
>
> Jon,
>
> There is a very big difference between fuzzy logic and
> fuzzy sets. I approve of fuzziness in set membership,
> but not fuzziness in truth value.
No argument there. The same thing applies to many-valued logics.
The important thing is not the multitude M of functional values that
we use in making decisions or in expressing propositions f : X -> M,
which need for analytic purposes, and can without loss of generality,
be constructed from distinctions of the form f : X -> B = {0, 1}, but
the arity, dimensionality, or valence of the relations that we use to
model the realities behind the phenomena. And here I think it is way
past time to put the interpreter back into the picture of logic and
semiotics, as they were forced to even in physics, long long ago.
Jon
> > Still, as I have suggested on numinous occasions, there is a good idea
> > lurking behind fussy sets, which are after all just triadic relations,
> > f : P x Q -> R, where P is a domain of elements, Q is a domain of sets,
> > and R is the real domain, and f(p, q) is the "degree of membership" of
> > the element p in the ordinary set q.
>
> The Lotfi one first invented fuzzy set theory and later extended it to fuzzy logic.
> Most of the useful applications of fuzziness use fuzzy set theory -- not fuzzy logic
> (which I criticize as an example of the fallacy of misplaced fuzziness).
>
> John
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