Re: Thomas' Fuzziness and Probability

From: S. F. Thomas (sfrthomas@yahoo.com)
Date: Fri Aug 17 2001 - 11:56:22 MET DST

  • Next message: Stephan Lehmke: "Re: Thomas' Fuzziness and Probability"

    Rich Ulrich <wpilib@pitt.edu> wrote in message
    news:<o4elntgdqdr1vb0gvtt7ng3leeraqp723m@4ax.com>...
    > On Wed, 15 Aug 2001 05:50:46 GMT, "Earl Cox" <earldcox1@home.com>
    > wrote:

    (( cuts ))

    >
    > Smithson's book gave me the impression of disparate
    > researchers, different models of "fuzzy logic," and a field
    > that was not unified to any great extent. A decade
    > later, is that different?

    Earl certainly refers to "fuzzy logic" in a way that would disregard
    what I and other researchers have contributed. Where all fuzzy
    researchers necessarily agree is that there exist terms in natural
    language with membership or characteristic function over a relevant
    domain such that some points in the domain have membership strictly
    between 0 and 1: there are degrees of membership. That is what
    fuzziness means. And that is where agreement pretty much ends.

    For the very basic concept of what operationally is this notion of
    degree of membership, and how to measure it, there is disagreement.
    And indeed, that is what started this thread. I take the view that
    fuzzy membership is really a form of semantic likelihood, a notion
    which explains in pretty straightforward terms what fuzziness is
    (st least in natural language semantics), and how it arises, given
    that even in calibrational settings, there is randomness in usage.

    The next point of disagreement relates to the choice of rules for
    connectives. Earl appears to champion the min-max rules. And the
    fact that these rules fail to obey law of excluded middle (LEM), and
    law of contradiction (LC) is trumpeted often as a virtue, and it
    is implied that fuzziness in itself *requires* that LEM and LC must
    fail.
    Here again, I for one disagree. I maintain that natural language
    fuzziness is not sufficient to cause LEM and LC to fail. For example,
    the term "tall" everyone would agree is fuzzy in the sense earlier
    described. But no witness would testify that her attacker was "tall
    and not tall"
    without inviting the derision of the court, and the fuzziness of the
    term will not come to her rescue. I conclude that LC holds in natural
    language even for fuzzy terms. Clearly, Earl has a different take on
    the matter, but I have been pointing out this simple thought
    experiment for a long time now, and I have encountered not a word in
    response from anyone suggesting I am wrong. Fuzziness does not failure
    of LEM or LC entail.

    Moreover, I and other researchers have shown how, within a fuzzy set
    theory, purely as a matter of uninterpreted mathematics, LEM and LC
    may be upheld.

    > Does fuzzy logic have to be *very* carefully tailored
    > to a particular problem?

    This is not a point of principle. All models are "wrong" by their
    very nature. Some, however, are useful. So the goodness of a
    model is never an absolute, there are always other considerations
    that enter, economy for one. So I would not attack "fuzzy logic"
    from this angle. Instead, like Wittgenstein, I seek the "logical
    clarification of thoughts", and I apply the same attitude to
    Bayes, for example, and to classical stats, both of which can be
    useful, even when philosophical foundations are far from settled.

    Regards,
    S. F. Thomas

    ############################################################################
    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



    This archive was generated by hypermail 2b30 : Fri Aug 17 2001 - 12:14:03 MET DST