Multicriteria decision analysis in a decision tree

The outcomes at the tips of a decision tree cannot always be represented by a single numerical value on a one dimensional axis. In many decision problems they are multidimensional, and their performance is expressed in a mixture of verbal statements and physical or monetary values. We propose to use the scores of cardinal methods for multicriteria decision analysis in order to represent the relative performance of the outcomes. Thereafter, we evaluate the chance forks in the tree via the corresponding aggregation procedure: in the Multiplicative AHP via weighted geometric means of the scores and in SMART via weighted arithmetic means. The procedure is based on the idea that the numerical values of verbal quantifiers such as somewhat more, more, ... do not depend on what we compare, whether it is relative importance or relative likelihood.