# Re: Grid-partitioning Fuzzy Systems

Subject: Re: Grid-partitioning Fuzzy Systems
From: Jorge Casillas (J.Casillas@decsai.ugr.es)
Date: Tue Oct 03 2000 - 19:49:20 MET DST

Hi Robert!!

In my opinion, you could understand "grid-partitioning" from two
different angles:

* Grid-partitioning when LEARNING the Fuzzy System: The operation mode
of some learning approaches involves using a grid (wich can be fuzzy or
crisp) defined by the input variable fuzzy partitions to bracket the
example data set into subspaces and obtaining one or several fuzzy rules

representing the behavior of such subspaces exclusively considering the
examples located in the corresponding subspace (the called positive
examples). The below figures show this process.

[Image][Image]

The first figure illustrates a fuzzy grid and the number of rules where
a specific example will contribute to derive it. The examples lying in
white zones have an influence on the generation of one rule, the ones
lying in light grey zones influence two rules, and the ones lying in
dark grey zones influence four rules. Once obtained the group of example

to consider in each region, the second figure illustrate the learning
process.

* Grid-partitioning as one of the interesting features developed by
Fuzzy Systems: Another point of view is refered to one of the most
interesting features developed by a Fuzzy System, the interpolative
reasoning. This characteristic plays a key role in the high performance
of Fuzzy Systems and is a consequence of the cooperation among the fuzzy

rules composing the Knowlege Base. As it is known, the output obtained
from an Fuzzy System is not usually due to a single fuzzy rule but to
the cooperative action of several fuzzy rules that have been fired
because they match the system input to any degree. This fact is due to
the grid-partitioning.

Best regards,

Jorge Casillas

robert_wilhelm_land wrote:

> Would someone kindly give a practical example for the usage of a
> Grid-partitioning Fuzzy System?
>
> Thinking of "grid" - I would associate something in the direction of
> image processing/recognition.
>
> Even any short comment would be helpful
>
> Robert
>
> ######
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```--
----------------------------------------------------
Jorge Casillas
Dep. of Computer Science and Artificial Intelligence
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Fax (office): +34-958-243317
mailto:J.Casillas@decsai.ugr.es
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