Using convex preference cones in multiple criteria decision making and related fields

This paper reviews our own and colleagues’ research on using convex preference cones in multiple criteria decision making and related fields. The original paper by Korhonen, Wallenius, and Zionts was published in Management Science in 1984. We first present the underlying theory, concepts, and method. Then we discuss applications of the theory, particularly for finding the most preferred alternative, finding a partial and total rank ordering of alternatives, as well as developing algorithms for solving multi-objective integer and other optimization problems

Convex cone-based partial order for multiple criteria alternatives

In this paper, we consider the problem of finding a preference-based strict partial order for a finite set of multiple criteria alternatives. We develop an approach based on information provided by the decision maker in the form of pairwise comparisons. We assume that the decision maker's value function is not explicitly known, but it has a quasi-concave form. Based on this assumption, we construct convex cones providing additional preference information to partially order the set of alternatives. We also extend the information obtained from the quasi-concavity of the value function to derive heuristic information that enriches the strict partial order. This approach can as such be used to partially rank multiple criteria alternatives and as a supplementary method to incorporate preference information in, e.g. Data Envelopment Analysis and Evolutionary Multi-Objective Optimization