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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