**Previous message:**Herman Rubin: "Re: Thomas' Fuzziness and Probability"**Maybe in reply to:**Joe Pfeiffer: "Thomas' Fuzziness and Probability"**Next in thread:**S. F. Thomas: "Re: Thomas' Fuzziness and Probability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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############################################################################ This message was posted through the fuzzy mailing list. (1) To subscribe to this mailing list, send a message body of "SUB FUZZY-MAIL myFirstName mySurname" to listproc@dbai.tuwien.ac.at (2) To unsubscribe from this mailing list, send a message body of "UNSUB FUZZY-MAIL" or "UNSUB FUZZY-MAIL yoursubscription@email.address.com" to listproc@dbai.tuwien.ac.at (3) To reach the human who maintains the list, send mail to fuzzy-owner@dbai.tuwien.ac.at (4) WWW access and other information on Fuzzy Sets and Logic see http://www.dbai.tuwien.ac.at/ftp/mlowner/fuzzy-mail.info (5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail/index.html

**Next message:**S. F. Thomas: "Re: Thomas' Fuzziness and Probability"**Previous message:**Herman Rubin: "Re: Thomas' Fuzziness and Probability"**Maybe in reply to:**Joe Pfeiffer: "Thomas' Fuzziness and Probability"**Next in thread:**S. F. Thomas: "Re: Thomas' Fuzziness and Probability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

*
This archive was generated by hypermail 2b30
: Sat Aug 18 2001 - 09:24:09 MET DST
*