Re: Imprecise Probability


Subject: Re: Imprecise Probability
From: Ellen Hisdal (ellen@ifi.uio.no)
Date: Sun Nov 19 2000 - 23:03:44 MET


> 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.
>
> Otto

The use of `high probability', `low probability' etc. was suggested by
Zadeh long ago. I think it was in the paper

@article{zoutline,
   author = {Zadeh, L.A.},
   title = {Outline of a New Approach to the Analysis of Complex
              Systems and Decision Processes},
   journal = {IEEE Transactions on Systems, Man and Cybernetics},
   year = {1973},
   volume = {SMC-3},
   ignored = {footnote p. 31. Use of multiplication instead of min for AND.
              Mentioned in my book in file intro.tex, sect. 1.7.3.},
   pages = {28-44} } .

He simply defines a fuzzy set `high' or `low' over the interval [0,1].

Personally I have an idea that in most cases one can just as well use a
numerical estimate of a probability value, such as .85 for `high',
>.15 for `low'. A fuzzy set over the interval [0,1] makes all
calculations more complicated. And probably this use of uncertainty in
an uncertainty value does not really have important advantages
over a definite probability value between 0 and 1 (which also expresses
an uncertainty in the occurrence of the given event).

So when somebody tells you
`there is a high probability of a given event',
you can simply replace this by
`there is a probability of .85 for the event'.

Greetings,
            Ellen

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