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.
Read more about this topic: Possibility Theory
Famous quotes containing the words possibility, theory, imprecise and/or probability:
“Twentieth-century art may start with nothing, but it flourishes by virtue of its belief in itself, in the possibility of control over what seems essentially uncontrollable, in the coherence of the inchoate, and in its ability to create its own values.”
—A. Alvarez (b. 1929)
“Every theory is a self-fulfilling prophecy that orders experience into the framework it provides.”
—Ruth Hubbard (b. 1924)
“... nothing is more human than substituting the quantity of words and actions for their character. But using imprecise words is very similar to using lots of words, for the more imprecise a word is, the greater the area it covers.”
—Robert Musil (1880–1942)
“Liberty is a blessing so inestimable, that, wherever there appears any probability of recovering it, a nation may willingly run many hazards, and ought not even to repine at the greatest effusion of blood or dissipation of treasure.”
—David Hume (1711–1776)