Towards sophisticated decision models: nonadditive robust ordinal regression for preference modeling

This paper addresses a methodology for decision support under multiple and correlated decision criteria. Nonadditive robust ordinal regression (NAROR) aims to build capacities that fit the decision makers’ explicit preferences and pairwise rankings of some alternatives. The capacities provide great flexibility to model decision problems accounting for interactions among the decision criteria. The feasible set of capacities helps identifying all the necessary and possible dominance relations among all the decision alternatives. In this paper we enhance the NAROR method by identifying optimal capacities through entropy maximisation. We formulate suitable optimisation problems and provide avenues for capacity simplification based on k-interactivity. We also consider the situation of large number of sparse constraints, for which we formulate a linear program based on Renyi entropy. We deal with preferences inconsistency by using multiple goal linear programming technique. The results show that the k-interactivity is an efficient way to reduce the complexity of capacities while preserving their expressiveness and representation ability, and that optimal capacities can be found by standard mathematical programming techniques.