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From: sthomas@decan.com (S. F. Thomas)
Subject: Re: Fuzzy logic compared to probability
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Date: Thu, 7 Mar 1996 17:45:50 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.fuzzy:6944 sci.stat.math:9628

Fred A Watkins (fwatkins@hyperlogic.com) wrote:
: sthomas@decan.com (S. F. Thomas) wrote:

: >Darren J Wilkinson (D.J.Wilkinson@durham.ac.uk) wrote:
: >: -----BEGIN PGP SIGNED MESSAGE-----

: >: S. F. Thomas (sthomas@decan.com) wrote:

: >> [ ... MUCH deleted material ... ]

<snip>
: Chuckle. Nice shot.

<snip>

: Hearty guffaw. Quite right, professor.

<snip>

: Har! Three times running!

<smiling despite myself> Praises gratefully accepted...

: >I happen to agree that the attempt to assert fuzziness as something
: >totally unrelated to probability is ultimately misguided.  But 
: >that is not the same thing as saying that fuzzy *is* probability.
: >As I have argued, here and elsewhere, there is rather a sort of
: >duality linking fuzzy and probability, in exactly the same
: >way that likelihood and probability are distinct, but related
: >concepts.  In any case, fuzzy and probability do not necessarily
: >compete, except when both retreat into a sort of solipsistic
: >subjectivism, where everything becomes a matter of personal taste.

: Well, here I might differ somewhat. I say the difference is
: definition, or lack of it. 

Quite.  If I have to choose between an (operationally) undefined, 
though intuitively appealing concept (Zadeh's original notion of 
grade of membership), and one which can yield the
same results sought by the undefined one, but which is
operationally well defined, and furthermore well grounded
in what is objectively observable (word usage in the 
context of the language-use phenomenon) I choose the latter.
When, furthermore, it leads to a unification between
the fuzzy and probability concepts, while making clear
the limits of applicability of the two concepts... well...

: Perhaps the numerics are similar (the big
: demand the probabilists must have and the fuzzyists can reject is
: summability, which has many implications) but the concepts differ.
                                                    ^^^^^^^^^^^^^^^
Again... quite.

: To baldly assert that probability correctly models ill-defined events
: (ultimately every event in reality, if we are strict Boolean
: logicians) takes an act of faith. But the Bayesians are good at
: belief, so I am told.

I can only agree.

If strongly enough held, some prior notions are immune from
reality, however at variance the prior notions may be
from what reality reveals.  It is a measure of the Bayesian
approach, that such behavior would be deemed "coherent" and
"consistent".  But would it be rational?

: >The essential stratagem revealed -- making of a bug, a feature.
: >I do not deny the importance of subjective belief in certain
: >situations.  But to take this ounce of truth, and to make of it
: >the whole inferential meal, is, again, sidestepping the essential
: >problem of inference, which is to characterize what *the data*
: >say.

: Yes!

Thank you.

: >: --
: >: Darren Wilkinson  -  E-mail: d.j.wilkinson@durham.ac.uk 
: >: <a href=http://fourier.dur.ac.uk:8000/djw.html>WWW page</a>

: >Regards,
: >S. F. Thomas

: Congratulations. It's good to see that someone can see through the fog
: a bit.

Again thanks.

: Fred A Watkins

Regards,
S. F. Thomas

