Explaining Hierarchical Multi-linear Models

Abstract

We are interested in the explanation of the solution to a hierarchical multi-criteria decision aiding problem. We extend a previous approach in which the explanation amounts to identifying the most influential criteria in a decision. This is based on an influence index which extends the Shapley value on trees. The contribution of this paper is twofold. First, we show that the computation of the influence grows linearly and not exponentially with the depth of the tree for the multi-linear model. Secondly, we are interested in the case where the values of the alternatives are imprecise on the criteria. The influence indices become thus imprecise. An efficient computation approach is proposed for the multi-linear model.