Decision Making with Interval Influence Diagrams
  In previous work (Fertig and Breese, 1989; Fertig and Breese, 1990) we
defined a mechanism for performing probabilistic reasoning in influence
diagrams using interval rather than point-valued probabilities. In this paper
we extend these procedures to incorporate decision nodes and interval-valued
value functions in the diagram. We derive the procedures for chance node
removal (calculating expected value) and decision node removal (optimization)
in influence diagrams where lower bounds on probabilities are stored at each
chance node and interval bounds are stored on the value function associated
with the diagram's value node. The output of the algorithm are a set of
admissible alternatives for each decision variable and a set of bounds on
expected value based on the imprecision in the input. The procedure can be
viewed as an approximation to a full e-dimensional sensitivity analysis where n
are the number of imprecise probability distributions in the input. We show the
transformations are optimal and sound. The performance of the algorithm on an
influence diagrams is investigated and compared to an exact algorithm.
