Identifying and ranking a most preferred subset of alternatives in the presence of multiple criteria

In this article an interactive method is developed to identify and rank a most preferred subset, T, of alternatives assuming that the decision maker has an implicit quasiconcave nondecreasing utility function. The method requires the decision maker to compare pairs of selected alternatives. Based on the responses of the decision maker, convex cones are constructed to eliminate alternatives that are proved to be inferior to alternatives in set T. The method aims at keeping the number of pairwise comparisons small. Computational experience with the method indicates that the required number of pairwise comparisons to form set T is usually small. However, the number of pairwise comparisons needed to confirm that this set is best may be large.