Re: Grid-partitioning Fuzzy Systems


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


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
> 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.
> ...

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
> 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.

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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