An interactive rectangle elimination method for biobjective decision making

This paper presents a new man-machine interactive method for biobjective decision making. It is specifically designed to cope with both the ill-defined nature of the decision problem and the high cost of computation points in the tradeoff (Pareto optimal) set. With this method, the decision maker may efficiently approximate the tradeoff set and/or estimate his preferred objective value. First, the notion of a rectangle representation of the tradeoff set by a set of points, called experiments, and a set of rectangles, defined by the experiments, is introduced. Next, a special class of decision makers is considered. For a decision maker in this special class, the rectangle representation of the tradeoff set defines a rectangle of uncertainty that contains the decision maker´s preferred objective value. A measure of the worst ease uncertainity is formulated and minimized to yield an optimal strategy for interactively selecting experiments. Finally, this strategy is employed in a general interactive algorithm that works under minimal assumptions on the tradeoff set and on the decision maker.