Possibility theory is a new form of information theory which is related to but independent of both fuzzy sets and probability theory. Technically, a possibility distribution is a normal fuzzy set (at least one membership grade equals 1). For example, all fuzzy numbers are possibility distributions. However, possibility theory can also be derived without reference to fuzzy sets.

The rules of possibility theory are similar to probability theory, but use either MAX/MIN or MAX/TIMES calculus, rather than the PLUS/TIMES calculus of probability theory. Also, possibilistic NONSPECIFICITY is available as a measure of information similar to the stochastic ENTROPY.

Possibility theory has a methodological advantage over probability theory as a representation of nondeterminism in systems, because the PLUS/TIMES calculus does not validly generalize nondeterministic processes, while MAX/MIN and MAX/TIMES do.

For further information, see:

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.