Theories and an exact interactive paired-comparison approach for discrete multiple-criteria problems

An interactive approach is developed to help decision-makers (DMs) find the best alternatives with few questions without making stringent assumptions about their behavior. Theories and procedures are developed for ranking alternatives and eliminating suboptimal ones, assuming that the DM can respond to tradeoff- and paired-comparison questions. It is assumed that the DM wishes to maximize an unknown quasiconcave utility function for discrete multiple-criteria decision-making (MCDM) problems. Several tests are developed based on convex dominating cones. Optimality conditions for discrete MCDM problems are given for extreme, nonextreme, and convex-dominated points without requiring the DM to enumerate the remaining set of discrete alternatives. These optimality conditions are based on a branching technique which converts nonextreme points to extreme points. This substantially reduces the number of questions asked of the DM. Finally, an exact discrete MCDM method is developed