Approximating incompletely defined utility functions of qualitative multi-criteria modeling method DEX

Decision analysis is aimed at supporting people who make decisions in order to satisfy their needs and objectives. The method called DEX is a qualitative multi-criteria decision analysis approach that provides support to decision makers in evaluating and choosing decision alternatives by using discrete attributes and rule-based utility functions. In this work, we extend our previous efforts of approximating complete, monotone DEX utility functions with methods Direct marginals, UTADIS and Conjoint analysis to incompletely defined utility functions. The experiments are performed both on functions obtained by solving real world decision making problems and on artificially created ones. The results show that all three methods provide accurate approximations of incompletely defined DEX utility functions, when the evaluation is done only on rules present in these incompletely defined functions. Among the three methods, the Conjoint analysis method generally has the best performance, however it is closely followed by the Direct marginals method. The Conjoint analysis method also achieves a better performance in approximating fully defined DEX utility functions by using incompletely defined instances of those functions. The UTADIS method performs comparatively well with functions having a high percentage of missing values.