Solving multiple criteria choice problems by interactive trichotomy segmentation

The paper describes a method for multiple criteria choice problems with an explicitly given but relatively large set of alternatives. The approach can be placed between methods with a priori specification of the decision maker's (DM's) preferences and interactive procedures. The method presented includes some interaction with the DM, but is based on an assumption that, at the beginning of the solution process, he/she has already relatively well-defined preferences. The DM's preferences are modeled with an outranking relation in the neighborhood of a reference profile in the non-dominated set. This preference model is used in order to define a trichotomy of the non-dominated set in terms of accepting good alternatives, rejecting non-interesting ones and defining alternatives that can neither be accepted, or rejected based on the available preference information. The method stops if the class of good alternatives is sufficiently small and if the DM is able to select one of them as the best compromise. Otherwise, the DM can modify the preferential information by changing either the reference profile, or the thresholds used to build the outranking relation. In other words, the DM defines dynamically the three categories. The description of the procedure is followed by presentation of an application.