**Subject: **Re: Imprecise Probability

**From: **Ellen Hisdal (*ellen@ifi.uio.no*)

**Date: **Sun Nov 19 2000 - 23:03:44 MET

**sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Breezy: "Re: Defuzzification"**Previous message:**Gert de Cooman: "Re: Imprecise Probability"**Maybe in reply to:**Otto Cordero: "Imprecise Probability"**Next in thread:**Breezy: "Re: Imprecise Probability"**Maybe reply:**Ellen Hisdal: "Re: Imprecise Probability"

*> Hello
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*>
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*> I would like to be more specific about my previous question....
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*> Lets supose someone is asked to give his estimation about the probability of
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*> some event, answers like "0.78 of probability" are very unlikely. I would
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*> expect something as "high probability" or "low probability", here we
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*> linguistic terms, wich could be associated with fuzzy sets.
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*> I am asking for more information on how fuzzy sets theory joins with
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*> probabilty theory to manage this kind of situations.
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*>
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*> Thanks a lot.
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*>
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*> Otto
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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
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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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**Next message:**Breezy: "Re: Defuzzification"**Previous message:**Gert de Cooman: "Re: Imprecise Probability"**Maybe in reply to:**Otto Cordero: "Imprecise Probability"**Next in thread:**Breezy: "Re: Imprecise Probability"**Maybe reply:**Ellen Hisdal: "Re: Imprecise Probability"

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