**Subject: **Re: Probability and possibility

**From: **Gert de Cooman (*Gert.DeCooman@rug.ac.be*)

**Date: **Fri Nov 10 2000 - 17:35:55 MET

**sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Lise Stoyell: "convex combination of linguistic labels"**Previous message:**WSiler@aol.com: "Re: literature on fuzzy logic in AI"**Maybe in reply to:**Jean-Philippe Drecourt: "Probability and possibility"**Next in thread:**Marco A. Vera: "RE: Probability and possibility"**Maybe reply:**Gert de Cooman: "Re: Probability and possibility"

*> I would like to get a clear explanation of the difference between possiblity
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*> measure and probability measure. In other words, I would like to know the
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*> answer to the question: "What possibility can do that probability cannot".
*

I think there are a number of ways in which this question could be

answered, depending on the interpretation that is given to both the

probability and the possibility measures. I will only discuss the case

here that these are interpreted as epistemic uncertainty models, that

is, models reflecting the "knowledge" or "beliefs" of an agent. In this

case, there is a standard argument by Bayesians (originating in de

Finetti's and Ramsey's work) called a Dutch book argument, claiming to

show that any rational agent should model his beliefs using a

probability measure. There is one questionable assumption in this

argument, stating essentially that a rational agent, whatever his

knowledge is, should always prefer one of two given options. He is not

allowed to refrain from making a choice between them, because for

instance he would not have not enough information to make an informed

choice (there is a difference between choice and preference, preference

implies choice, but a choice can be arbitary and not based on

preference, e.g. if it is enforced as in the Bayesian argument). If this

questionable rationality requirement is removed, and the other

rationality requirements are kept, we find that an agent's beliefs

should be modeled not necessarily by a probability measure, but by what

is called a coherent (i.e. rational) *imprecise* probability model. A

specific example of such a model is a coherent upper probability, and

normal possibility measures are specific examples of such coherent upper

probabilities (as are probability measures, of course). So in this view,

possibility measures and probability measures are just special cases of

a much more general class of models that are available for modelling

beliefs and knowledge. The more information is available, the more

choices an agent will be willing to actually make, and the more precise

(i.e. the closer to a probability measure) his model becomes.

Possibility measures are uncertainty models that are fairly imprecise,

meaning that they reflect weak information states. It has been argued

that the information conveyed by statements in natural language is

fairly weak, and can be modelled by possibility measures.

You can find more information on imprecise probability models in the web

site http://ippserv.rug.ac.be.

More information on the connection between possibility measures and

(imprecise) probability theory can also be found in a few of my papers,

cited below. Many of these can be downloaded form my web site

(ippserv.rug.ac.be/~gert)

I hope this clarifies at least one side of this issue.

Best wishes,

Gert de Cooman

Gert de Cooman and Dirk Aeyels, A random set description of a

possibility measure and its natural extension, 6 pages, accepted for

publication in IEEE Transactions on Systems, Man and Cybernetics, 1999.

Gert de Cooman and Dirk Aeyels, Supremum preserving upper probabilities,

Information Sciences, 1999, vol. 118, pp. 173-212.

Peter Walley and Gert de Cooman, Coherence of rules for defining

conditional possibility, International Journal of Approximate Reasoning,

1999, vol. 21, pp. 63-107.

Gert de Cooman and Peter Walley, An imprecise hierarchical model for

behaviour under uncertainty, 34 pages, submitted for publication in

Theory and Decision, 1999

Gert de Cooman, Integration and conditioning in numerical possibility

theory, 29 pages, submitted for publication in Annals of Mathematics and

Artificial Intelligence, 1999.

-- ============================================================== Prof. dr. ir. Gert de Cooman Onzekerheidsmodellering en systeemtheorie/ Uncertainty modelling and systems theory -------------------------------------------------------------- E-mail: gert.decooman@rug.ac.be URL: http://ippserv.rug.ac.be/~gert -------------------------------------------------------------- Universiteit Gent Onderzoeksgroep SYSTeMS Technologiepark - Zwijnaarde 9 9052 Zwijnaarde Belgium -------------------------------------------------------------- Tel: +32-(0)9-264 56 53 Fax: +32-(0)9-264 58 40 ==============================================================############################################################################ This message was posted through the fuzzy mailing list. (1) To subscribe to this mailing list, send a message body of "SUB FUZZY-MAIL myFirstName mySurname" to listproc@dbai.tuwien.ac.at (2) To unsubscribe from this mailing list, send a message body of "UNSUB FUZZY-MAIL" or "UNSUB FUZZY-MAIL yoursubscription@email.address.com" to listproc@dbai.tuwien.ac.at (3) To reach the human who maintains the list, send mail to fuzzy-owner@dbai.tuwien.ac.at (4) WWW access and other information on Fuzzy Sets and Logic see http://www.dbai.tuwien.ac.at/ftp/mlowner/fuzzy-mail.info (5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail/index.html

**Next message:**Lise Stoyell: "convex combination of linguistic labels"**Previous message:**WSiler@aol.com: "Re: literature on fuzzy logic in AI"**Maybe in reply to:**Jean-Philippe Drecourt: "Probability and possibility"**Next in thread:**Marco A. Vera: "RE: Probability and possibility"**Maybe reply:**Gert de Cooman: "Re: Probability and possibility"

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