Re: Elkan crisis

From: Ulrich Bodenhofer (ulrich.bodenhofer@scch.at)
Date: Thu May 17 2001 - 03:49:56 MET DST

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    Don't believe anybody who calls that a crisis! Elkan's statement was simply
    a dull error. He, more or less, assumed that fuzzy logic obeys all laws of
    Boolean algebras (which is not true) and proved, under these FALSE
    assumptions, that it collapses into Boolean logic. Read the original Elkan
    paper
    (it is somewhere on the Web, for sure) and you will understand
    (since you seemingly have read Ruspini's reply already).

    The question arises whether something which is not a Boolean algebra
    may be considered as a concept of logic. Nowadays, the accepted opinion
    is yes! I would not like to go into detail, but to recommend the following
    books:

    @book{Gottwald:01,
      author = {S. Gottwald},
      title = {A Treatise on Many-Valued Logics},
      publisher = {Research Studies Press},
      address = {Baldock},
      year = {2001},
      series = {Studies in Logic and Computation}
    }

    @book{Hajek:98,
      author = {P. H\'ajek},
      title = {Metamathematics of Fuzzy Logic},
      publisher = {Kluwer Academic Publishers},
      volume = {4},
      series = {Trends in Logic},
      address = {Dordrecht},
      year = {1998}
    }

    @book{NovakPerfilievaMockor:99,
      author = {V. Nov\'ak and I. Perfilieva and J. Mo\v{c}ko\v{r}},
      title = {Mathematical Principles of Fuzzy Logic},
      publisher = {Kluwer Academic Publishers},
      address = {Boston},
      year = {1999}
    }

    Regards,
    Ulrich

    "T.T." <TOMASO.TOSOLINI@UD.NETTUNO.IT> wrote in message
    news:3AF2F5AF.1FE9B66C@UD.NETTUNO.IT...
    > 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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