Decision Trees with Single and Multiple Interval-Valued Objectives

Important to decision making is recognition of what today's decisions have on future options, and an oft-used tool to aid in this problem is the decision tree. This paper addresses situations in which uncertainty arises in the objectives associated with different sequential decision paths and provides a decision tree for uncertain parameters where only bounds, not distributions, are known. Single- and multiple-objective interval-valued decision trees are introduced. Interval arithmetic is used for the decision tree rollback process. To address the difficulty of an interval-valued comparison of alternatives, several decision rules, as well as a probabilistic approach, are discussed in the decision tree context. The interval-valued decision trees are deployed in a simple maintenance, repair, and overhaul decision-making illustration.