Re: Grid-partitioning Fuzzy Systems


Subject: Re: Grid-partitioning Fuzzy Systems
From: Jorge Casillas (J.Casillas@decsai.ugr.es)
Date: Wed Oct 11 2000 - 01:51:22 MET DST


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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.

I hope this help you.

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
University of Granada, E-18017, Granada, SPAIN
Phone (office / home): +34-958-242376 / 257614
Fax (office): +34-958-243317
mailto:J.Casillas@decsai.ugr.es
http://decsai.ugr.es/~casillas

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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.
 


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.

I hope this help you.

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

############################################################################
This message was posted through the fuzzy mailing list.
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"SUB FUZZY-MAIL myFirstName mySurname" to listproc@dbai.tuwien.ac.at
(2)  To unsubscribe from this mailing list, send a message body of
"UNSUB FUZZY-MAIL" or "UNSUB FUZZY-MAIL yoursubscription@email.address.com"
to listproc@dbai.tuwien.ac.at
(3)  To reach the human who maintains the list, send mail to
fuzzy-owner@dbai.tuwien.ac.at
(4)  WWW access and other information on Fuzzy Sets and Logic see
http://www.dbai.tuwien.ac.at/ftp/mlowner/fuzzy-mail.info
(5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail/index.html

--
----------------------------------------------------
Jorge Casillas
Dep. of Computer Science and Artificial Intelligence
University of Granada, E-18017, Granada, SPAIN
Phone (office / home): +34-958-242376 / 257614
Fax (office): +34-958-243317
mailto:J.Casillas@decsai.ugr.es
http://decsai.ugr.es/~casillas
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