Re: Fuzzy * Fuzzy

From: Alexander Podvesovsky (alex@podv.bitmcnit.bryansk.su)
Date: Sun Feb 11 2001 - 08:03:43 MET

  • Next message: Paul Victor Birke: "Re: Fuzzy * Fuzzy"

    Dear Otto,

    8-Feb-01 17:43 you wrote:

    > A generic membership functions has the form [x1, x2] --> [y1, y2], where x1,
    > x2, y1 and y2 are real numbers in most of the cases. I am interested in
    > those particular cases where the axis of the membership function are not
    > crisp but fuzzy (for example: if [x1, x2] or [y1, y2] are fuzzy intervals or
    > if their elements are fuzzy numbers).

    > I would appreciate if you point out any publication regarding the
    > mathematical treatement of this kind of membership functions defined in
    > terms of fuzzy elements.

    You seem to talk on so-called fuzzy sets of type 2. There are quite
    a few publications concerning this subject. You can see for example:

    L.A.Zadeh, The concept of a linguistic variable and its application to
    approximate reasoning, American Elsevier Publishing, New York, 1973.

    M.Mizumoto and K.Tanaka, Some properties of fuzzy sets of type 2,
    Information and Control, 31 (1976), 312-341.

    R.R.Yager, Fuzzy subsets with uncertain membership grades, IEEE Trans.
    on Systems, Man and Cybernetics, 14 (1984), 271-275.

    Hope it helps,

    --
    Alexander Podvesovsky		   mailto: alex@podv.bitmcnit.bryansk.su
    

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