Modeling criteria and project interactions in portfolio decision analysis with the Choquet integral

We present a general framework to deal with multicriteria portfolio decision analysis problems in which between-projects independence or within-project independence do not necessarily hold. The Choquet integral preference model is a non-additive integral widely used in multicriteria decision analysis to take into account the possible interactions between criteria. In this case, we apply the Choquet integral, on the one hand, to deal with the interactions between criteria used to evaluate the projects and, on the other hand, to take into account the interactions between projects in the portfolio global evaluation. To reduce the number of parameters necessary to define the considered preference model and keep the problem tractable, we use the 2-additive Choquet integral that assigns a value to each entity and to each pair of entities only. An example shows how to apply our proposal to a multicriteria portfolio decision analysis problem.