Fuzzy measure theory considers a number of special classes of measures, each of which is characterized by a special property. Some of the measures used in this theory are plausibility and belief measures, fuzzy set membership gratings and the classical probability measures. In the fuzzy measure theory, the conditions are precise, but the information about an element alone is insufficient to determine which special classes of measures to be used. The central concept of fuzzy measure theory is fuzzy measure, which was introduced by Sugeno in 1974.

Axioms

Fuzzy measure can be consider as Generalization of the classical probability measure. A fuzzy measure g over a set X (the universe of discourse with the subsets E, F...) satisfies the following conditions when X is finite:

1. when E is an empty set then g(E)=0.

2. g(X)=1.

3. when E is a sub-set of F, then g(E)<g(F).

also see Probability theory, Possibility theory

links

http://pami.uwaterloo.ca/tizhoosh/measure.htm

References

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