Re: Books or papers about Fuzzy Approximation Theorem


Subject: Re: Books or papers about Fuzzy Approximation Theorem
From: Fred A Watkins (fwatkins@hyperlogic.com)
Date: Sun Apr 09 2000 - 09:35:09 MET DST


KS <ks@lycos.com> wrote:

>Hi!
>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.

Kosko's FAT holds for a real function defined on a compact subset of Rn
(n-dimensional real space). The theorem holds for additive-style systems
in particular, and some others as well. The proof is a direct construction
based on uniform continuity. Obvious generalizations certainly exist but
are not presently in the literature.

Fred A Watkins, Ph.D.
HyperLogic Corporation
PO Box 300010
Escondido, CA 92030-0010 USA
voice: +1 760 746 2765 x 9117
fax: +1 760 746 4089
email: fwatkins@hyperlogic.SNIP_THIS_OUT.com

Decode email address to contact me.

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