How to Handle Missing Values in Multi-Criteria Decision Aiding?

How to Handle Missing Values in Multi-Criteria Decision Aiding?

Christophe Labreuche, S├ębastien Destercke

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence
Main track. Pages 1756-1763. https://doi.org/10.24963/ijcai.2019/243

It is often the case in the applications of Multi-Criteria Decision Making that the values of alternatives are unknown on some attributes. An interesting situation arises when the attributes having missing values are actually not relevant and shall thus be removed from the model. Given a model that has been elicited on the complete set of attributes, we are looking thus for a way -- called restriction operator -- to automatically remove the missing attributes from this model. Axiomatic characterizations are proposed for three classes of models. For general quantitative models, the restriction operator is characterized by linearity, recursivity and decomposition on variables. The second class is the set of monotone quantitative models satisfying normalization conditions. The linearity axiom is changed to fit with these conditions. Adding recursivity and symmetry, the restriction operator takes the form of a normalized average. For the last class of models -- namely the Choquet integral, we obtain a simpler expression. Finally, a very intuitive interpretation is provided.
Keywords:
Knowledge Representation and Reasoning: Knowledge Representation and Decision ; Utility Theory
Knowledge Representation and Reasoning: Preference Modelling and Preference-Based Reasoning
Agent-based and Multi-agent Systems: Cooperative Games