Reducing Interval-Valued Decision Trees to Conventional Ones: Comments on Decision Trees with Single and Multiple Interval-Valued Objectives

Decision trees are an excellent tool for choosing between alternatives, where the likely financial outcomes of making a particular decision are usually measured by real numbers. To describe the uncertainty of outcomes, the notion of interval-valued decision trees was recently introduced, where only the lower and upper bounds of an outcome, described by an interval, are known. To address the difficulty of an interval-valued comparison of alternatives, several decision rules, including the Laplace and Hurwicz rules, have been discussed in the literature. In this paper, we show that in terms of such decision rules, the decision making for interval-valued decision trees can be equivalently reduced to real-valued ones, which means that an alternative is chosen at some decision node in the original interval-valued decision tree if and only if it is chosen at the same decision node in the corresponding real-valued decision tree. In this way, we develop an approach to solving interval-valued decision tree problems with the analysis technique for traditional decision trees.