Fuzzy Measure Theory
The concave integral over large spaces
Fuzzy Sets and Systems
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Information consisting of probabilities of some (but possibly not all) events induces an integral with respect to a probability specified on a subalgebra. A decision maker evaluates the alternatives using only the available information and completely ignoring unavailable information. Assume now that the decision maker assesses the worth of a different lottery at each point in a discrete time. Assume also that each such lottery is preferred to some fixed alternative lottery. Now, consider the situation where the sequence of lotteries converges in some sense. If the limiting lottery is preferred to the fixed alternative, then the preference order is referred to as time continuous. This paper studies time continuity for two preference functionals: the Choquet integral and the integral with respect to a probability specified on a subalgebra. The integral with respect to probability specified on a subalgebra is determined by the structure of the available information. By relating it to the Choquet integral, we characterize the structure of available information that would yield time continuity.