Re: Fuzzy projections and cylindrical extensions

jg.campbell (jg.campbell@ulst.ac.uk)
Mon, 26 Jul 1999 12:28:37 +0200 (MET DST)

In article <001b01bed4e5$ec8549b0$7e10000a@satishj.sasi.com>,
fuzzy-mail@dbai.tuwien.ac.at wrote:

> I was trying to understand Fuzzy projections from the meterial that I
=
> have - Not so descriptive. Can some body please explain the concept
more =
> descriptively or give pointers towards some papers, tutorial =
> books,applications etc.
>

Better than most textbooks:

1. Robert Fulle'r's Notes on Neuro Fuzzy Systems:

http://www.abo.fi/~rfuller/nfs.html

2. Rene' Jager's PhD thesis:

http://www.born-again.demon.nl/phd.html

(to print either of these, you will need a PostScript printer).

Book:

author = "J-S.R. Jang and C-T. Sun and E. Mizutani",
title = "Neuro-fuzzy and Soft Computing",
publisher = "Prentice Hall",
year = "1997"

Example, let's say you have a fuzzy set on H(eight) and W(eight),
A(verage) whose membership is

mA(h, w) = 1 at height = 68 in., weight = 140 lb

and which decreases as |h-68|, |w-140| increases

You can use the projection to get the fuzzy set on h, mAH(h) of average
height; one form of projection (the only?) is

mAH(h) = max [mA(h, w)]
all w

The cylindrical extension does the opposite -- creates (e.g.) a
two-dimensional fuzzy set out of a one-d. one.

Hope this helps,

Jon Campbell

--
Jonathan G Campbell Univ. Ulster Magee College Derry BT48 7JL N. Ireland
+44 1504 375367 JG.Campbell@ulst.ac.uk  http://www.infm.ulst.ac.uk/~jgc/

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