An outranking relation built on an additive value function preference model: Creating synergy between both paradigms

Abstract

In multiple criteria decision making, the additive value function model is useful for modeling weak-order preferences, quantitative information about criterion performance, and tradeoffs where disadvantages in some attributes can be compensated by improvements in others. However, major difficulties arise when the value function model must deal with ordinal information in some criteria, highly heterogeneous scales, unacceptably poor criterion performances, and threshold effects leading to intransitive preferences, issues that can be addressed by outranking methods. This paper aims to create synergy between these perspectives. Under certain conditions, the preference relation “at least as good as” can be represented by an additive multi-attribute value function on a subset of the decision set. The value function model can then be extrapolated out of this subset while retaining some information about the “worth” of alternatives which do not belong to it. By extrapolating the value function model and using some additional information, a transitive outranking relation (“the DM has sufficient reasons to justify that “x is at least as good as y and no strong reasons against”) can be defined on a wider subset of the decision set. Using the transitive outranking relation, methods for ranking and ordinal classification (recently called rating) problems are discussed, in which the transitivity of the relation is a valuable feature. Ordinal and measurable value functions are distinguished. In the latter case, the outranking relation is richer, so the cardinality of the incomparability relation could be greatly reduced.