Interactive approaches for discrete alternative multiple criteria decision making with monotone utility functions

In this paper the authors develop interactive approaches for the discrete alternative multiple criteria decision making problem. They develop an algorithm that finds the most preferred alternative of a decision maker (DM) assuming only that the decision maker has a monotonicy 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. The authors also develop a more efficient version of the algorithm for the more restrictive case of a monotonic quasiconcave utility function. They present favorable computational results in terms of the required number of pairwise comparisons for both versions of the algorithm. The authors then develop a general algorithm that first identfies the type of the decision maker’s utility function and then employs the approach that is compatible with the identified utility function type. They also present computational results for the general algorithm.