Re: Fuzzy Pattern Recognition

Rainer Holve (
Thu, 21 May 1998 18:13:25 +0200 (MET DST)

> In a message dated 98-05-01 05:43:17 EDT, you note that the size of a fuzzy
> rule base tends to increase with the number of input variables, and ask how
> this can be dealt with in fuzzy pattern recognition. I can recall two
> possible approaches.
> 1) William Combs of Boeing in Seattle, USA has an approach which enables
> the number of rules to increase linearly with the number of input
> variables rather than as the square.

Actually, the number of possible rules grows exponentially with the number of
inputs, i.e. n inputs with m fuzzy sets -> m^n rules.

What one could do about this "curse of dimensionality" [Bellman] (and what I do
:) ) is to use n-1 2-dimensional rulebases instead of one n-dimensional and
arrange them as a binary tree. Some benchmarking with this stuff is already
done and it works quite well. If you are interested, you can download two
papers about it at