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 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 probability: any possibility distribution defines a unique set of admissible probability distributions by
This allows one to study possibility theory using the tools of imprecise probabilities.
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