Re: Books or papers about Fuzzy Approximation Theorem


Subject: Re: Books or papers about Fuzzy Approximation Theorem
From: Vladik Kreinovich (vladik@cs.utep.edu)
Date: Sun Apr 09 2000 - 18:30:11 MET DST


A survey of different universal approximation results (with an emphasis on control)
is in our chapter

  Vladik Kreinovich, George C. Mouzouris, and Hung T. Nguyen,
  "Fuzzy rule based modeling as a universal control tool'',
  In: H. T. Nguyen and M. Sugeno (eds.),
  Fuzzy Systems: Modeling and Control,
  Kluwer, Boston, MA, 1998, pp. 135-195.
  
A soft version of this chapter (not the final one, but close) can be downloaded
from
  <A HREF="ftp://cs.utep.edu/pub/reports/tr96-49a.tex">file in LaTeX</A>,
  uses <A HREF="ftp://cs.utep.edu/pub/reports/crckapb.sty">crckapb.sty</A>

You are also welcome to look at

  Vladik Kreinovich, Hung T. Nguyen, and Yeung Yam,
  "Fuzzy Systems Are Universal Approximators for a Smooth Function
  And Its Derivatives",
  International Journal of Intelligent Systems, 2000 (to appear).
  <A HREF="http://www.cs.utep.edu/vladik/1999/tr99-2.ps">PostScript file</A>.

> Does anyone know of good books or papers or web sites where I can find
> informations (either for beginners or with maths) on the Fuzzy
> Approximation Theorem (FAT) which I read in a book from Kosko for
> beginners, which says that a fuzzy system can approximate any
> (continuous) function. I would liike to know exactly under what
> hypothesis this happens, the kind of fuzzy systems, limitations on the
> kind of the approximated functions and some math theory behind this.
> Thank you!
> email: skywalker_73@yahoo.com.

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