RE: Max-Min Inference and Triangular / Trapezoidal membership functions

From: P. Sarma (psarma@seas.upenn.edu)
Date: Tue Mar 26 2002 - 16:15:33 MET

  • Next message: Fractal A.: "Re: Max-Min Inference and Triangular / Trapezoidal membership functions"

    There's a lot of work distributed, here and there, over the literature
    on such things. Mizumoto has done a lot of numerical and semi-analytical
    work on it (see Fuzzy Control Systems, Kandel and Langholz, eg.).
    Semi/numerical results suggest strongly that the modelling similarities
    are strong. I am sure many FLS/C researchers might concur - I can
    personally verify that FLC's used for some (strongly) nonlinear models
    in some of my work consistently show no (easily) discernible difference
    for these 2 fuzzy inference models (FIM).

    It could be expected that there will be some finite, even if small,
    numerical differences. In that case, one could argue that there are
    always a large range of free/tuning parameters (eg. MF parameters) in a
    FLS/NFLS, to "compensate" for this. In that case, it's generally
    (computationally) better to choose the Max-Prod, or Max-Dot FIM. (And,
    cite the UFA property as "defense"). The Max-Prod is smooth (Max-Min
    causes nonsmooth clipping), and allows easier formulation of, and
    solution by, a gradient-like operator for training.

    Pramit

    -----Original Message-----
    From: fuzzy-mail@dbai.tuwien.ac.at [mailto:fuzzy-mail@dbai.tuwien.ac.at]
    On Behalf Of Daniel Fortin
    Sent: Saturday, March 16, 2002 3:43 AM
    To: Multiple recipients of list
    Subject: Max-Min Inference and Triangular / Trapezoidal membership
    functions

    I was wondering if anyone could tell me what the advantages and or
    disadvantages of using max-min and max product inferencing are. I'm
    using Fuzzy and Neural Approaches in Engineering by Tsoukalas and
    Uhrig and it doesn't seem to describe any of the design tradeoffs for
    selecting a fuzzy inferencing method. Also, what are the tradeoffs
    between using triangular and trapezoidal membership functions?

    If anyone could answer these questions I'd really appreciate it.

    Thanks in advance!

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