# Re: Significance of overlapping output functions

jg.campbell (jg.campbell@qub.ac.uk)
Wed, 8 Dec 1999 15:41:51 +0100 (MET)

In article <000001bf4093\$eda8dc20\$8301f080@black.ncl.ac.uk>,
fuzzy-mail@dbai.tuwien.ac.at wrote:
> I am using FL for a choice model. For the purposes of my PhD thesis, I

Could you explain what is meant by a "choice model"?

need
> to be able to explain (to my non-FL professor) the significance of any
> overlaps in the output function (i.e. areas where output from two or
more
> rules overlaps). My assumption is that any overlaps are accounted for
in the
> fuzzy union function, provided that the union function is idempotent.
Is
> this correct?

I have no idea -- I say so because I'm unsure if either point is
relevant. BTW, is it possible for a two place function to be idempotent?

>
> I would be grateful for any refernces that cover this topic.
>

If you are talking about a relatively classical fuzzy control (or
function approximation problem) -- fuzzifier ... fuzzy rule-base which
maps fuzzy sets to fuzzy sets ... defuzzifier, then, to get the
_interpolation_ that is at the core of this form of fuzzy logic, you
must have overlap of adjacent sets in both input and output partitions.

Another way of looking at this form of "fuzzy logic" is as a fuzzy graph
-- mapping fuzzy sets to fuzzy sets -- see either of Zadeh articles
below. The fuzzy graph model should be accessible to your ("non FL")
prof.

title = "Fuzzy Logic, Neural Networks, and Soft Computing",
journal = "Communications of the ACM",
year = "1994",
volume = "37",
number = "3",
pages = "77--86",
month = mar
}

title = "Soft Computing and Fuzzy Logic",
journal = "IEEE Software",
year = "1994",
volume = "11",
number = "6",
pages = "48--56",
month = nov
}

Best regards,

Jon Campbell

--
Jonathan G. Campbell, School of Computer Science, The Queen's University
of Belfast, BT7 1NN  Tel +44 028 90 274623  jg.campbell@qub.ac.uk
http://strule.cs.qub.ac.uk/~jongc

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