Robust ranking of multi-criteria alternatives using value functions compatible with holistic preference information

We present two recent methods,called UTAGMS and GRIP,from the viewpoint of robust ranking of multi-criteria alternatives.In these methods,the preference information provided by a single or multiple Decision Makers(DMs)is composed of holistic judgements of some selected alternatives,called reference alternatives.The judgements express pairwise comparisons of some reference alternatives(in UTAGMS),and comparisons of selected pairs of reference alternatives from the viewpoint of intensity of preference(in GRIP).Ordinal regression is used to find additive value functions compatible with this preference information.The whole set of compatible value functions is then used in Linear Programming(LP)to calculate a necessary and possible weak preference relations in the set of all alternatives,and in the set of all pairs of alternatives.While the necessary relation is true for all compatible value functions,the possible relation is true for at least one compatible value function.The necessary relation is a partial preorder and the possible relation is a complete and negatively transitive relation.The necessary relations show consequences of the given preference information which are robust because "always true".We illustrate this methodology with an example.

We present two recent methods, called UTAc＇Ms and GRIP, from the viewpoint of robust ranking of multi-criteria alternatives. In these methods, the preference information provided by a single or multiple Decision Makers （DMs） is composed of holistic judgements of some selected alternatives, called reference alternatives. The judgements express pair,vise comparisons of some reference alternatives （in UTA^GMS） , and comparisons of selected pairs of reference alternatives from the viewpoint of intensity of preference （in GRIP）. Ordinal regression is used to find additive value functions compatible with this preference information. The whole set of compatible value functions is then used in Linear Programming （LP） to calculate a necessary and possible weak preference relations in the set of all alternatives, and in the set of all pairs of alternatives. While the necessary relation is true for all compatible value functions, the possible relation is true for at least one compatible value function. The necessary relation is a partial preorder and the possible relation is a complete and negatively transitive relation. The necessary relations show consequences of the given preference information which are robust because ＂always true＂. We illustrate this methodology with an example.