Interactive Approaches for Discrete Alternative Multiple Criteria Decision Making with Monotone Utility Functions

In this paper we develop interactive approaches for the discrete alternative multiple criteria decision making problem. We develop an algorithm that finds the most preferred alternative of a decision maker (DM) assuming only that the DM has a monotonic utility function. The algorithm divides the criteria space into a number of smaller subspaces and then uses the ideal points of these subspaces to eliminate alternatives. We also develop a more efficient version of the algorithm for the more restrictive case of a monotonic quasiconcave utility function. We present favorable computational results in terms of the required number of pairwise comparisons for both versions of the algorithm. We then develop a general algorithm that first identifies the type of the DM's utility function and then employs the approach that is compatible with the identified utility function type. We also present computational results for the general algorithm.