XPost: comp.soft-sys.matlab
From: not@here.com
"Dmitry A. Kazakov" wrote in message
news:1y2599uy74umw.sllstdc5wvou.dlg@40tude.net...
> On Sat, 16 Apr 2005 12:22:49 +0100, Fuzzy wrote:
>
> > The examples I've seen in the fuzzy world all relate to categorising one
> > item of data at a time.
> > Are there any straightforward "standard" paradigms out there to classify
a
> > data item based on grouped data results?
> >
> > For example, say I have this training data set.
> >
> > X =1,2,1,3,4,2,4,1 (interval category)
> > Y= 3,6,3,6,8,3,4,1 (response)
> >
> > As we can see from this toy data the highest or "best" response may be
seen
> > to be around 4 tailing away from this.
> >
> > So, when I have a new data item to classify, say a 3, I can give a
> > prediction for its response. Linguistically, I would wish to classify as
a
> > "Preference", Say "most preferred", "neutral", "least preferred" - I
know
> > how to defuzz, I'm just stating this to give a flavour of what I'm
after.
> >
> > I know I can use standard distribution stats such as mean and standard
> > deviation, but I wondered how the fuzzy world would view this problem.
In
> > fact would a method be to formulate the fuzzy sets based on such
> > distribution stats.
> >
> > Any thoughts, references etc appreciated.
>
> To apply fuzzy you need to formulate the problem in fuzzy terms. The
> problem of approximation of a function is not automatically fuzzy. Neither
> it is statistical. It might become statistical first when Y(X) is
> considered as a random variable with some distribution and the goal is to
> find the parameters of the distribution which would minimize the
> probability of an error. This is how we come to mean and dispersion,
> regression, least squares etc. Alternatively the meaning could be a
> distance treated as, say, energy of a physical process and again the
result
> might be least squares etc. Nothing changes here with fuzzy. It might
> become fuzzy if for instance, the values of X and Y are fuzzy, or the
> function is searched in a class of fuzzy-valued functions etc. Once you
> have a fuzzy formulation of the problem, "preference" receives a meaning.
> Then you can expect Y*(3) yielding a fuzzy number. The membership function
> of this number would represent the expectations of particular numbers to
be
> members of true Y(3). Most preferred would be ones with the highest truth
> values.
Hi,
Say X and Y are imprecise. Does this make them fuzzy?
As I have historic values of X and Y, can this data not be used to derive
some sort of fuzzy system - with perhaps the aid of expert knowledge to
clarify the system, given the historic data.
If I take a toy example off the top of my head. Say different cattle are
presented with different feed and we wish to distinguish the preference a
given cow has for a given feed as measured by the milk yield. We cannot
compare yield accross Cows.
The feed is just grass, and the difference is how green it is as described
by an "expert". So there may be some imprecision when fresh grass is
presented.
We have the raw stats for previous cattle and we have a new batch of grass
that has had its greenness allocated by the expert.
Given the above, on a cow by cow basis, I wish a metric of how much the cow
will prefer and/or dislike the feed. The estimation of the magnitude of the
preference/dislike will be aided by the amount of historic data we have do
support any estimation.
For example, a cow may only have rarely been presented with "brown" grass
although the yied implies she may prefer it, but we cannot categorically say
this given the lack of prior data - or perhaps we may wish to extrapolate
this preference given the cows liking for grass close to this colour.
I can see this can be done (or hope anyway), but what are the method(s) used
to be able to translate the historic data so that it becomes meaningful in
this context?
I hope that makes sense - maybe not :)
TIA
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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