An Interval-Valued Utility Theory for Decision Making with Dempster-Shafer Belief Functions
This work addresses decision-making under ambiguity for fields like AI and economics, but it is incremental as it builds on existing theories like von Neumann-Morgenstern and Jaffray's frameworks.
The paper tackles the problem of decision-making under uncertainty with Dempster-Shafer belief functions by developing an axiomatic utility theory, resulting in interval-valued utilities and a partial preference order for belief function lotteries.
The main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern's utility theory for probabilistic lotteries as described by Luce and Raiffa. Unlike the probabilistic case, our axiomatic framework leads to interval-valued utilities, and therefore, to a partial (incomplete) preference order on the set of all belief function lotteries. If the belief function reference lotteries we use are Bayesian belief functions, then our representation theorem coincides with Jaffray's representation theorem for his linear utility theory for belief functions. We illustrate our representation theorem using some examples discussed in the literature, and we propose a simple model for assessing utilities based on an interval-valued pessimism index representing a decision-maker's attitude to ambiguity and indeterminacy. Finally, we compare our decision theory with those proposed by Jaffray, Smets, Dubois et al., Giang and Shenoy, and Shafer.