Re: Imprecise Probability


Subject: Re: Imprecise Probability
From: Paul Victor Birke (nonlinear@home.com)
Date: Wed Nov 15 2000 - 13:56:41 MET


Otto Cordero wrote:
>
> Hello
>
> I would like to be more specific about my previous question....
> Lets supose someone is asked to give his estimation about the probability of
> some event, answers like "0.78 of probability" are very unlikely. I would
> expect something as "high probability" or "low probability", here we
> linguistic terms, wich could be associated with fuzzy sets.
> I am asking for more information on how fuzzy sets theory joins with
> probabilty theory to manage this kind of situations.
>
> Thanks a lot.
***************************
Dear Otto

I am not aware of any theory here but have not looked for a number of
years. In 1995 I have to >>invent<< the representation. Define your
crisp probability via cdf. Define Lower and Upper estimates for P=1.0
and P=0.5 and P=0.0. Do the same using UltraLow and UltraHigh where you
are confident the probability ranges stops, for sure. Again the
UltraHigh and UltraLow are needed to be estimated for P=1.0 P=0.5 and
P=0. The actual Fuzzy Probability ranges between Low and High as a
Uniform Distribution. There are linear descending skirts between Low
and UltraLow and High and UltraHigh. Notice the cdf for the sides could
be more like Weibull and nonGaussian in shape. Another observation
which is direct result of independent estimates of Low High UltraLow
UltraHigh and there probabilities with respect to the main x axis. In
my case this axis was Price.

Paul V. Birke, P. Eng.
NN Researcher in Guelph ON CANADA

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