Dempster-Shafer Structures, Monotonic Set Measures and Decision Making

Abstract

We first formulate the problem of decision making under uncertainty. The importance of the representation of our knowledge about the uncertainty in formulating a decision process is pointed out. We provide a brief discussion of the case of probabilistic uncertainty. Next, in considerable detail, we discuss the case of decision making under ignorance. For this case the fundamental role of the attitude of the decision maker is noted and its subjective nature is emphasized. Next the case in which a Dempster-Shafer belief structure is used to model our knowledge of the uncertainty is considered. Here we also emphasize the subjective choices the decision maker must make in formulating a decision function. The case in which the uncertainty is represented by a monotonic set measure is then investigated. We then return to the Dempster-Shafer belief structure and show its relationship to the set measure. This relationship allows us to get a deeper understanding of the formulation the decision function used Dempster- Shafer framework. We discuss how this deeper understanding allows a decision analyst to better make the subjective choices needed in the formulation of the decision function. Finally we provide a generalized framework for decision-making in the face of Dempster-Shafer type uncertainty.