Artificial Intelligence
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 non-probabilistic uncertainty and its applications
A decision theory for non-probabilistic uncertainty and its applications
The Dempster--Shafer calculus for statisticians
International Journal of Approximate Reasoning
Decision making on the sole basis of statistical likelihood
Artificial Intelligence
Decision making in the TBM: the necessity of the pignistic transformation
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Classic Works of the Dempster-Shafer Theory of Belief Functions
Classic Works of the Dempster-Shafer Theory of Belief Functions
Statistical decisions using likelihood information without prior probabilities
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Decision making with partially consonant belief functions
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Linear utility theory for belief functions
Operations Research Letters
Decision with Dempster--Shafer belief functions: Decision under ignorance and sequential consistency
International Journal of Approximate Reasoning
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Partially consonant belief functions (pcb), studied by Walley, are the only class of Dempster-Shafer belief functions that are consistent with the likelihood principle of statistics. Structurally, the set of foci of a pcb is partitioned into non-overlapping groups and within each group, foci are nested. The pcb class includes both probability function and Zadeh's possibility function as special cases. This paper studies decision making under uncertainty described by pcb. We prove a representation theorem for preference relation over pcb lotteries to satisfy an axiomatic system that is similar in spirit to von Neumann and Morgenstern's axioms of the linear utility theory. The closed-form expression of utility of a pcb lottery is a combination of linear utility for probabilistic lottery and two-component (binary) utility for possibilistic lottery. In our model, the uncertainty information, risk attitude and ambiguity attitude are separately represented. A tractable technique to extract ambiguity attitude from a decision maker behavior is also discussed.