Decision making under measure-based granular uncertainty

In situations, where an uncertain variable takes its value in a large space, we can use granulation of the space to simplify the knowledge acquisition process. We observe, however, that this use of granulation can come at the price of introducing imprecision into the related decision process. We note that answers to questions about values related to the original space can often only be answered using interval values. We look at two classes of decision problems where uncertain information about relevant variables is expressed indirectly via information about the uncertainty on related granular objects. To make a precise decision, we require the decision maker to provide some subjective preference information to resolve the interval uncertainty induced by the granulation. In this paper, our major contribution is that we provide an approach to decision making in the face of uncertainty where the uncertain information is expressed on a space of granular objects and the underlying uncertainty is most generally represented by a measure.