An interactive approach for inverse multiple criteria sorting problem

Multiple criteria sorting is the problem of assigning objects that are evaluated on multiple criteria to ordered classes. In inverse multiple criteria sorting problem, the assignment of objects to classes is known. The decision maker (DM) can implement actions to improve the scores of objects on criteria, thus enabling the assignment of objects to better classes.

In inverse multiple criteria sorting problems, two types of questions arise: (1) What is the set of actions that will result in the desired classification with minimum cost? and 2) What is the set of actions to obtain the best classification without exceeding a predetermined budget? There exist two versions for each question: (i) Simple version, where the parameters of the sorting method are known and (ii) Robust version, where the parameters are not fully known.

In this article, we focus on the case where the DM does not provide any budget limitation or desired classifications a priori. By implementing more actions, that is, by spending more money, better classifications may be obtained. We aim to analyse the trade-off between cost and classification, and determine the set of actions that will result in the most preferred cost-classification compromise by the DM. We develop an approach that proceeds interactively with the DM, and determines such most preferred set of actions. The developed approach assumes the simple version and uses MR-Sort as sorting model. We provide a detailed illustrative example on a real life problem and present the progress of the interactive algorithm.