Artificial Intelligence
On the possibilistic decision model: from decision under uncertainty to case-based decision
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - A special issue on fuzzy measures
Dempster belief functions are based on the principle of complete ignorance
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - special issue on models for imprecise probabilities and partial knowledge
A decision theory for partially consonant belief functions
International Journal of Approximate Reasoning
Linear utility theory for belief functions
Operations Research Letters
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This paper examines proposals for decision making with Dempster-Shafer belief functions from the perspectives of requirements for rational decision under ignorance and sequential consistency. The focus is on the proposals by Jaffray & Wakker and Giang & Shenoy applied for partially consonant belief functions. We formalize the concept of sequential consistency of an evaluation model and prove results about sequential consistency of Jaffray-Wakker's model and Giang-Shenoy's model under various conditions. We demonstrate that the often neglected assumption about two-stage resolution of uncertainty used in Jaffray-Wakker's model actually disambiguates the foci of a belief function, and therefore, makes it a partially consonant on the extended state space.