**Subject: **Re: Grid-partitioning Fuzzy Systems

**From: **robert_wilhelm_land (*robert_wilhelm_land@csi.com*)

**Date: **Wed Oct 11 2000 - 01:45:05 MET DST

**sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Brian Carse: "CFP: FLAIRS 2001 Special Track on Neural Networks and Fuzzy Systems Applications"**Previous message:**Gregory L. Hansen: "Fuzzy Control"**Maybe in reply to:**robert_wilhelm_land: "Grid-partitioning Fuzzy Systems"**Next in thread:**Jorge Casillas: "Re: Grid-partitioning Fuzzy Systems"**Maybe reply:**robert_wilhelm_land: "Re: Grid-partitioning Fuzzy Systems"

Jorge Casillas wrote:

*> In my opinion, you could understand "grid-partitioning" from two
*

*> different angles:
*

*>
*

*> * Grid-partitioning when LEARNING the Fuzzy System: The operation mode
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*> of some learning approaches involves using a grid (wich can be fuzzy or
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*> crisp) defined by the input variable fuzzy partitions to bracket the
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*> example data set into subspaces and obtaining one or several fuzzy rules
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*>
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*> representing the behavior of such subspaces exclusively considering the
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*> examples located in the corresponding subspace (the called positive
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*> examples). The below figures show this process.
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*> ...
*

Jorge, thank you very much for spending so much time on this inquiry.

This first point of view is very good understandable and in fact quite

logical to me (at least I think so).

But:

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

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

This is completely unkown to me. What axactly is a Knowledge Base in a

fuzzy system, how does it act or how is this data combined with the

system in whole?

Then, there's a webpage

http://pikas.inf.tu-dresden.de/~fritzke/FuzzyPaper/node1.html#SECTION00010000000000000000

which gives a example at the bottom (figure 4) using 2-dimensional

data (which in fact I do not understand either, does it mean data out

of different R^n?) and which puzzles me completely - defining a 4x3

grid containing 12 rules - is this simular to the image you sent

explaining your first view point?

Would be really grateful for some more help

Best Regards,

Robert

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**Next message:**Brian Carse: "CFP: FLAIRS 2001 Special Track on Neural Networks and Fuzzy Systems Applications"**Previous message:**Gregory L. Hansen: "Fuzzy Control"**Maybe in reply to:**robert_wilhelm_land: "Grid-partitioning Fuzzy Systems"**Next in thread:**Jorge Casillas: "Re: Grid-partitioning Fuzzy Systems"**Maybe reply:**robert_wilhelm_land: "Re: Grid-partitioning Fuzzy Systems"

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