New Advances on Multiple Criteria Hierarchy Process and the Choquet integral preference model

Abstract

In Multiple Criteria Decision Aiding, a set of alternatives is evaluated on a family of criteria to deal with a choice, sorting or ranking problem. Not always the evaluation criteria are sited at the same level and, moreover, some type of interaction between criteria can be observed. To deal with the interaction between criteria, non-additive integrals and, in particular the Choquet integral, are used in literature. In this thesis we considered the hierarchy of criteria and the interaction between criteria issues. In particular, regarding the hierarchy of criteria, we extended the sorting method UTADIS and the Choquet integral preference model to deal with decision making problems presenting an hierarchy of criteria using the Multiple Criteria Hierarchy Process, recently introduced in literature. In both cases, an indirect way of providing preference information has been taken into account considering, for the extension of the UTADIS method, the Robust Ordinal Regression (ROR) while, for the extension of the Choquet integral preference model, ROR and Stochastic Multiobjective Acceptability Analysis (SMAA). With respect to the interaction between criteria, we considered two ways of building a common scale necessary for the application of the Choquet integral. On one hand, we introduced an heuristic while, on the other hand, we applied the very well-known AHP method. Moreover, we proposed a new method, called NEMO-Ch, applying for the first time, the Choquet integral to the Evolutionary Multiobjective Optimization field. The new method permits to address the search to the region of the Pareto front most interesting for the Decision Maker, taking into account her/his preferences.