A progressive multiple criteria sorting approach based on additive utility functions considering imprecise information

This paper presents a progressive approach for assigning alternatives that are defined by multiple criteria into a set of ordered categories. It extends the UTADIS method to take into account two types of imprecise assignment information and allow the DM to provide preference information in an interactive way. In this approach, a heuris-tic algorithm is given to build and update the DM's global utility function and then a mixed integer linear programming model is developed to identify the inconsistency of the DM's assignment information in the iterative process. When inconsistency occurs, the conicting assignment results are presented to the DM to help him modify his previous information. However, when the information is consistent, the fittest category and the range of possible categories on each alternative are obtained for the DM. The fittest cat-egory is computed through the previous mixed integer linear programming model, and the range of possible categories is inferred by another two mixed integer linear programming models. Meanwhile, the rationality of the latter two mixed integer linear programming models is also justified theoretically. Finally, an example of MBA programs is given as an illustration of the proposed approach.