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

Abstract

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.

An operational test for existence of a consistent increasing quasi-concave value function

“…The existence of a value function with some pre-specified properties is a very old and important problem; See, e.g., Birkhoff [3], Debreu [4], Fishburn [5], Karsu [6], Keeney and Raiffa [7], Köksalan et al [8], Korhonen et al [9,10,11,12], Nasrabadi et al [13], and Zionts et al [16]. To the best of our knowledge, except for Korhonen et al [11], there is no study about the existence of quasi-concave order-preserving value functions.…”