# Re: Necessity / Possibility Measure

From: Manolis Wallace (wallace@image.ntua.gr)
Date: Sat Apr 20 2002 - 21:24:53 MEST

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Hello Anna

I wonder whether you are familiar with belief and plausibility measures. If yes,
then the answer is this: necessity is the counterpart of beleif and possibility
is the counterpart of plausibility in possibility theory. Possibility theory is a
special branch of evidence theory that deals only with bodies of evidence whose
focal elements are nested.

The following are true.
Nec(A intersection B)=min(Nec(A),Nec(B))
Pos(A union B)=max(Pos(A),Pos(B))

This is a simple way to think of them:
Necessity for A is the sum of probabilities for every element that is contained
in A.
Possibility for A is the sum of probabilities for every element that contains A.

For more you can check out Klir G. and Bo Yuan, Fuzzy Sets and Fuzzy Logic,
Theory and Applications, New Jersey, Prentice Hall, 1995

I hope this helps.
Manolis

Anna Wortmann wrote:

> Hello,
>
> can somebody explain to me what the necessity and possibility measures are?
> I am looking for a descriptive explanation.
>
>
> Anna Wortmann
>
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```--
Manolis Wallace
Image, Video & Multimedia Systems Laboratory
Department of Electrical & Computer Engineering
National Technical University of Athens
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