Decision-Making with Belief Functions: a Review
This is an incremental review paper that synthesizes existing methods for decision-making under uncertainty, primarily relevant to researchers in belief functions and imprecise probabilities.
The paper reviews decision-making methods under uncertainty within the belief function framework, showing that most blend criteria for decision under ignorance with Bayesian expected utility principles, and highlights the need for deeper investigation into fundamental issues and assessment of different approaches.
Approaches to decision-making under uncertainty in the belief function framework are reviewed. Most methods are shown to blend criteria for decision under ignorance with the maximum expected utility principle of Bayesian decision theory. A distinction is made between methods that construct a complete preference relation among acts, and those that allow incomparability of some acts due to lack of information. Methods developed in the imprecise probability framework are applicable in the Dempster-Shafer context and are also reviewed. Shafer's constructive decision theory, which substitutes the notion of goal for that of utility, is described and contrasted with other approaches. The paper ends by pointing out the need to carry out deeper investigation of fundamental issues related to decision-making with belief functions and to assess the descriptive, normative and prescriptive values of the different approaches.