Talk:Possibility theory


 * Unlike probability theory which is based on signal-signal measure,

What does the above mean? I've taught probability theory at four different universities, MIT among them, and I can't make heads or tails out of the above. Michael Hardy 23:45, 4 Mar 2005 (UTC)

This still needs cleanup, but there was considerable confusion with Dempster Shafer theory of evidence.

Minh

Please don't write things like


 * $$min\{\,a,b,c\,\}.$$

Correct notation is


 * $$\min\{\,a,b,c\,\}.$$

Similarly, use backslahses in \inf, \sup, \det, \cos, \log, \exp, \lim, etc. Not only does this prevent italicization and provide proper spacing, but also in some cases makes subscripts appear directly under the operator rather than under and to the right. Michael Hardy 19:45, 28 Apr 2005 (UTC)

OK, checked. But shouldn't we use the same notation everywhere: either $$\Pi$$ or $$\operatorname{nec}$$ ?

Minh

I am not sure I am understanding the following:


 * It follows that, like probability, the possibility measure is determined by its behavior on singletons. 

It does not seem true. If we consider as probability space the Lebesgue measure in $$[0, 1]$$, every singleton has probability 0. The probability of any interval cannot be written as the sum of the probabilities of the singletons contained in it, because it is uncountable. User:zeycus 13:45, 06 May 2006 (UTC)


 * With any continuous probability distribution (of which the normal distribution---the one associated with the "bell-shaped curve"---is the most well known) every singleton has probability zero, and that does not determine the probability distribution---not even close. I have qualified the statement in the article. Michael Hardy 02:00, 7 June 2006 (UTC)


 * Ok, now that it is specified to hold only in the finite and countable cases I agree with the claim. User:zeycus 18:35, 07 May 2006 (UTC)

Example?
Could someone add an example to the thext, who understands this? Thank you --Gaborgulya 22:49, 15 May 2007 (UTC)

Please simplify this sentence
"'One way to interpret 0.5 in that proposition is to define its meaning as: I am ready to bet that it's empty as long as the odds are even (1:1) or better, and I would not bet at any rate that it's full.'" I would like to understand possibility theory as non native English. I understand every word, here but not the sentence. Could you please simplify?--80.99.91.196 (talk) 13:38, 24 November 2007 (UTC)

pos maps subsets of omega rather than elements of omega
In view of the axioms that pos should satisfy, it seems to me that function pos does NOT map elements (or: members) of the set Omega to [0,1], but it does map subsets of Omega to [0,1]. So, the currently defined type of pos is wrong. Is there an expert willing to change the text? —Preceding unsigned comment added by 130.89.12.118 (talk) 08:11, 10 March 2008 (UTC)

So what?
This looks a really interesting topic, but I'm struggling to answer the "So what?" question. Can anyone give examples of some possible practical or policy applications? Harry Woodroof 27 Mar 2009 —Preceding unsigned comment added by 86.156.25.229 (talk) 22:46, 27 March 2009 (UTC)

formula for intersection
In the text it says:
 * $$\operatorname{pos}(U \cap V) \geq \min \left( \operatorname{pos}(U), \operatorname{pos}(V) \right).$$

Shouldn't this be $$\leq$$? It seems this was the case for older versions of the page, and does make more sense if e.g. $$\operatorname{pos}(U)>0$$ and $$\operatorname{pos}(V)>0$$ and $$U\cap V=\varnothing$$. — Preceding unsigned comment added by SimonDeRidder (talk • contribs) 13:28, 19 March 2018 (UTC)

Change pos to \pi and \Pi
I think the \operatorname{pos} should be replaced with \pi and \Pi, whichever one is correct in every setting.

I can't find any current literature using pos short for possibility. The standard is pi, like in Reference #1 (DuboisPrade2002).

nec for necessity I have seen sometimes, but more often it is denoted simply N.

What do others think about this? ItDoesntFit (talk) 08:52, 20 July 2023 (UTC)