Conditional expectation for monotone measures, the discrete case

In modelling economic decision processes with risk and uncertainty one has to update the measures and condition the functions given new information. Non-additive measures (also called Choquet capacities) proved to be an important tool for modelling uncertainty. Here, for functions on a finite set Omega, a comprehensive approach to conditioning is made. It builds on conditional expectation for probability measures in representing the monotone measure nu as a min of belief functions below v and the latter as a max of additive measures in the core of the respective belief function. The same method is applied, too, for defining the product of monotone measures. (C) 2002 Elsevier Science B.V. All rights reserved.