An Interval-Valued Utility Theory for Decision Making with
  Dempster-Shafer Belief Functions
  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.
