On the Expected Value of Fuzzy Events

Generalizing a first approach by L. A. ZADEH (J. Math. Anal. Appl. 23, 1968), expected values of fuzzy events are studied which are (up to standard boundary conditions) only required to be monotone. They can be seen as an extension of capacities, i.e., monotone set functions satisfying standard boundary conditions. Some of these expected values can be characterized axiomatically, others are based on some distinguished integrals (Choquet, Sugeno, Shilkret, universal, and decomposition integral).