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.
