A progressive sorting approach for multiple criteria decision aiding in the presence of non-monotonic preferences

A new decision-aiding approach for multiple criteria sorting problems is proposed for considering the non-monotonic relationship between the preference and evaluations of the alternatives on specific criteria. The approach employs a value function as the preference model and requires the decision maker (DM) to provide assignment examples of a subset of reference alternatives as preference information. We assume that the marginal value function of a non-monotonic criterion is non-decreasing up to the criterion's most preferred level, and then it is non-increasing. For these non-monotonic criteria, the approach starts with linearly increasing and decreasing marginal value functions but then allows such functions to deviate from the linearity and switches them to more complex ones. We develop several algorithms to help the DM resolve the inconsistency in the assignment examples and assign non-reference alternatives. The algorithms not only incorporate the DM's evolving cognition of the preference, but also take into account the trade-offs between the capacity for satisfying incremental preference information and the complexity of the preference model. The DM is guided to evaluate the results at each iteration and then provides reactions for the subsequent iterations so that the proposed approach supports the DM to work out a satisfactory preference model. We demonstrate the applicability and validity of the proposed approach with an illustrative example and a numerical experiment.