Re: Elkan crisis

From: Vladik Kreinovich (vladik@cs.utep.edu)
Date: Fri May 11 2001 - 14:40:58 MET DST

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    Dear Tomaso, Your guess is correct.

    Elkan's premises were wrong, as a result although his theorem was technically
    correct (rather trivially so) it was in no way detrimental to fuzzy. There was
    no crisis and no shock in fuzzy community.

    Let me give you a little bit more details.

    Elkan assumed that if two propositional formulas are classically equivalent,
    they should get the same fuzzy value when interpreterd in fuzzy logic. Of
    course, this is not a correct premise, because, e.g., "a \/ not a" is
    classically equivalent to "true", but in the standard fuzzy logic with max as
    \/, the corersponding fuzzy value max(a,1-a) may be different from 1 (e.g., for
    a=0.5). Elkan has a slightly more complicated example, but just slightly.

    I am not saying that nothing good came out of Elkan's paper, the good thing is
    that several researchers in fuzzy community started thinking about when exactly
    propositional formulas are equivalent tin fuzzy logic and got some interesting
    results out of it, but overall, there was no shock at all.

    Vladik

    P.S. In addition to Ruspini's papers, you may want to read

    Hung T. Nguyen et al.
      "Is the success of fuzzy logic really paradoxical?
      Or: Towards the actual logic behind expert systems",
      International Journal of Intelligent Systems, 1996, Vol. 11,
      No. 5, pp. 295-326.

    and papers by Elbert and Carol Walkers.
    > Date: Mon, 7 May 2001 00:38:49 +0200 (MET DST)
    > Originator: fuzzy-mail@dbai.tuwien.ac.at
    > From: "T.T." <TOMASO.TOSOLINI@ud.nettuno.it>
    > To: nafips-l@sphinx.Gsu.EDU
    > Subject: Elkan crisis
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    >
    > Hello, I'm an italian student, and I read many docs over the net, about
    > the Elkan's crisis, that shocked the fuzzy community in 1993-94... , but
    > I couldn't understand if the problem has been solved ( or if there
    > wasn't any problem at all ). In fact reading Ruspini's reply seemed me
    > that the paper demostrated an incorrect theorem(in the sense that it's
    > premises were not correct, mantaining a correct proof.).
    > Thanks for every explanation or useful link(sorry for my english).
    >
    > --
    > Linux,
    > the choice of a GNU generation.
    >
    > Tomaso Tosolini
    > C.te Bellin, 9 - 33036 Mereto di T. (UD)
    > Italia
    >
    >
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