Re: Fuzzy Implication Rules with Fuzzy Input

From: albert@massivbau.tu-darmstadt.de
Date: Tue Jan 16 2001 - 03:57:12 MET

  • Next message: Vilem Novak: "Re: Fuzzy Implication Rules with Fuzzy Input"

    This is a comment to Dr. William Silers answer with additional
    questions:

    Dr. Siler wrote:
    > True implication operators such as you mention (NOT t-norms) are really
    > useless in this situation. The only thing that will work is a t-norm, such as
    > Mamdani uses.
    Why are they useless? In some articles e.g. Zadeh or
    Dubois/Prade have pointed out that for some applications
    (especially in expert systems) such operators are needed.

    > For example, suppose we have triangular membership functions for small and
    > big in rule "If x=small, then y=big". Suppose now that x is a fuzzy
    > triangular number with the same width as small, but offset so that in some
    > places x is zero but small is not, and in some places small is zero but x is
    > not. Then y will be a fuzzy number which is nowhere zero! If you don't
    > believe this, try it.
    I believe it, or rather I know that this is true. But as I mentioned
    before especially Dubois/Prade (e.g. in What are fuzzy rules and
    How to use them) justify this fact with their theory of gradual rules
    and certainty rules. A fuzzy number or rather a possibility
    distribution whose value is nowhere zero bears the information that
    every value is possible to a certain degree.

    > Don't use an implication operator - use a t-norm.
    Aren't there any applications for which you would recommend the
    use of implication operators??

    Best Regards
    Andrej Albert

    **********************************
        Dipl.-Ing. Andrej Albert
        Institut für Massivbau
        TU Darmstadt
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        Tel.: 06151/16-7036
        Fax : 06151/16-7034
    http://www.massivbau.tu-darmstadt.de/user/albert/web/default.htm
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