Editing Possibility theory (section)

==Possibility theory as an imprecise probability theory==
There is an extensive formal correspondence between probability and possibility theories, where the addition operator corresponds to the maximum operator.

A possibility measure can be seen as a consonant [[plausibility measure]] in the [[Dempster–Shafer theory]] of evidence. The operators of possibility theory can be seen as a hyper-cautious version of the operators of the [[transferable belief model]], a modern development of the theory of evidence.

Possibility can be seen as an [[upper and lower probabilities|upper probability]]: any possibility distribution defines a unique [[credal set]] of admissible [[probability distribution]]s by

::<math>K = \{\, P \mid \forall S\ P(S)\leq \Pi(S)\,\}.</math>

This allows one to study possibility theory using the tools of [[imprecise probability|imprecise probabilities]].