Re: Need proofs of approximation power of the 1st-order Sugeno systems

From: Vitaliy Kolodyazhniy (kolodyazhniy@ieee.org)
Date: Mon Sep 03 2001 - 14:07:37 MET DST

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    Dear Bruno and all other members of comp.ai.fuzzy and fuzzy mailing list who
    have contributed to answering my question,

    Thank you very much for your help and useful links.

    > You can look at: http://sipi.usc.edu/~kosko/
    > There you will be able to download:
    > - B. Kosko, S. Mitaim, "Adaptive Joint Fuzzy Sets for Function
    > Approximation",

    I have read these and some other papers on fuzzy approximation theorems. The
    question was related to the 1st-order Sugeno systems (with linear
    consequents). Approximation properties of such systems have been treated to
    much less extent, though they are a more powerful tool for non-linear system
    modelling.

    Special thanks to fsong, who gave me a clue where to find papers on this
    issue. The problem of proving the approximation properties of the 1st-order
    Sugeno systems seems to have been treated for the first time by Hao Ying.
    There are a lot of very useful downloadable papers at
    http://www.ece.eng.wayne.edu/~hying/

    Most of other results are related to the 0th-order Sugeno (with constant
    consequents) or alike models, which are, in fact, special types of Mamdani
    systems (with pre-defuzzified output membeship functions).

    > If you tell us (all people in this newsgroup) something more
    > in detail about what you are doing, somebody may come up with
    > some better idea.

    What I'm dealing with is control of nonlinear systems based on linearization
    of the 1st-order Takagi-Sugeno models. The models are being adapted online.
    They are somewhat similar to ANFIS and CANFIS, developed by J.-S. R. Jang,
    though I use my own real-time learning procedures with online rule
    generation. Everything is implemented in Matlab and seems to work fine. The
    work is almost finished, so I needed formal mathematical proofs for my
    thesis.

    Thanks to everyone.

    With best regards,
    Vitaliy Kolodyazhniy
    kolodyazhniy@ieee.org

    ----- Original Message -----
    From: Bruno Di Stefano <nuptek@sympatico.ca>
    To: Multiple recipients of list <fuzzy-mail@dbai.tuwien.ac.at>
    Sent: Sunday, September 02, 2001 2:30 PM
    Subject: Re: Need proofs of approximation power of the 1st-order Sugeno
    systems

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