# Re: Thomas' Fuzziness and Probability

From: Joe Pfeiffer (pfeiffer@cs.nmsu.edu)
Date: Sat Aug 18 2001 - 08:54:09 MET DST

• Next message: S. F. Thomas: "Re: Thomas' Fuzziness and Probability"

Ah, I think I've finally got it. Tell me if this rephrasing is what
you have in mind.

LC is only called into question if one accepts a fairly tortured
extension of LC into fuzzy logic: namely, ``if x has any membership
at all in A, x can have no membership in ~A.'' But it would be more
reasonable to define ~A as that set such that if x's membership in A
is m, x's membership in ~A is (1-m). Notice that this also gives us
LC for crisp sets as a special case.

In the example (and substituting what I believe to be more reasonable
phrasing -- the original phrasing got in the way of my understanding),
if the witness were to say that the assailant was ``tall but average''
it would be ridiculous, as that would be asserting membership of 1 in
both tall and (not tall)[see note below]. If the witness were to say
that the assailant was ``sort of tall and sort of average'' then she
would be asserting only that the assailant's membership in tall was in
(0,1), and his membership in (not tall) was also in (0,1). This would
be completely reasonable.

[note] As in my last post I assume ~tall == (short U average). If we
assume that any membership in tall implies no membership in short,
then any reasonable definition of union will give us that for anyone
with any membership at all in tall, ~tall = average.

PS: I'd like to comment, as the originator of this thread, that it
has done more to solidify my understanding of fuzzy logic than
everything I've read to date. Thanks to you all.

```--
Joseph J. Pfeiffer, Jr., Ph.D.       Phone -- (505) 646-1605
Department of Computer Science       FAX   -- (505) 646-1002
New Mexico State University          http://www.cs.nmsu.edu/~pfeiffer
SWNMRSEF:  http://www.nmsu.edu/~scifair
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