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From: sthomas@decan.com (S. F. Thomas)
Subject: Re: Fuzzy logic compared to probability
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Date: Thu, 29 Feb 1996 19:00:13 GMT
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Jive Dadson (jdadson@ix.netcom.com) wrote:
< snip >
: I agree completely that "fuzzy" as it is typically presented
: is about measurement and description. My question is, in what
: way does fuzzy differ from the kind of evidential generalization
: statisticians call "smoothing"? In particular, isn't a fuzzy support
: set precisely the same thing as a kernel or radial basis function?

: Are you familiar with the literature that develops smoothing,
: or rather constraints on crispness, as a consequence of
: Bayesian prior-beliefs concerning the kinds of functions that
: might model the unknown process being studied? Occam's razor is
: a anthropomorphic blade. I am just beginning a study of that

I'm not familiar with the literature to which you refer.  So
I'm afraid I can't answer your first question.  

: Finally, if fuzzy is substantively different from smoothing,
: could you give an example of an actual construct -- a computer
: program preferably -- which uses fuzzy to some purpose other
: than smoothing? I have made this request repeatedly, with no
: takers. I am genuinely interested, and would be pleased with
: a concrete example.

There are some examples in the book I've recently published
(Thomas, 1995).  See in particular Chap. VI, which deals
with possibilistic decision analysis (single-criterion,
multi-criterion, and group).  The broad approach taken is
to treat judgments of preference as part of a wider class
of subjective judgements generally, and methods are developed
which apply generally to the problem of subjective estimation
or scaling (for example of psycho-physical attributes -- man
as measuring device), and in particular to choice among
decision options.  Fuzzy is very helpful in this endeavor.  The
procedures are not obviously a form of "smoothing", but
have more to do with "combination of evidence".  It may
not be much of a stretch to construe the latter as somehow
being a case of the former.

:                  Best regards,
:                  Jive

Regards,
S. F. Thomas


