Possibility theory is a mathematical theory for dealing with certain types of uncertainty. It is closely related to fuzzy sets and fuzzy logic. Probability values are assigned to sets of possibilities, rather than single events. Zadeh first introduced possibility theory in 1978 in the context of fuzzy sets.

It allows for belief about propositions to be represented as intervals, taking on two values, Possible and Necessary, with

Possible ≤ Necessary.

It can be used to analyze evidence, etc.: the Dempster-Shafer theory is a possibility theory for dealing with evidence.

See also: logical possibility, Probability theory.

References

• Dubois, Didier, and Prade, Henri, Possibility Theory, Plenum Press, New York, 1988.

• Joslyn, Cliff, "Possibilistic Measurement and Set Statistics", in Proceedings of the 1992 NAFIPS Conference 2:458-467, NASA, 1992.

• Joslyn, Cliff, "Possibilistic Semantics and Measurement Methods in Complex Systems", in Proceedings of the 2nd International Symposium on Uncertainty Modeling and Analysis, Bilal Ayyub (editor), IEEE Computer Society 1993.

• Wang, Zhenyuan, and Klir, George J., Fuzzy Measure Theory, Plenum Press, New York, 1991.

• Zadeh, Lotfi, "Fuzzy Sets as the Basis for a Theory of Possibility", Fuzzy Sets and Systems 1:3-28, 1978.

External links

• http://lrb.cs.uni-dortmund.de/fd7/dubois.pdf