Paper Info
Title
Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions
Abstract
We present a new method, called UTAGMS, for multiple criteria ranking of alternatives from set A using a set of additive value functions which result from an ordinal regression. The preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives AR⊆A, called reference alternatives. The preference model built via ordinal regression is the set of all additive value functions compatible with the preference information. Using this model, one can define two relations in the set A: the necessary weak preference relation which holds for any two alternatives a, b from set A if and only if for all compatible value functions a is preferred to b, and the possible weak preference relation which holds for this pair if and only if for at least one compatible value function a is preferred to b. These relations establish a necessary and a possible ranking of alternatives from A, being, respectively, a partial preorder and a strongly complete relation. The UTAGMS method is intended to be used interactively, with an increasing subset AR and a progressive statement of pairwise comparisons. When no preference information is provided, the necessary weak preference relation is a weak dominance relation, and the possible weak preference relation is a complete relation. Every new pairwise comparison of reference alternatives, for which the dominance relation does not hold, is enriching the necessary relation and it is impoverishing the possible relation, so that they converge with the growth of the preference information. Distinguishing necessary and possible consequences of preference information on the complete set of actions, UTAGMS answers questions of robustness analysis. Moreover, the method can support the decision maker when his/her preference statements cannot be represented in terms of an additive value function. The method is illustrated by an example solved using the UTAGMS software. Some extensions of the method are also presented.
Year
DOI
Venue
2008
10.1016/j.ejor.2007.08.013
European Journal of Operational Research
Keywords
Field
DocType
Multiple criteria ranking,Ordinal regression approach,Additive value function
Pairwise comparison,Preference relation,Mathematical optimization,Ranking,Regression analysis,Preorder,Ordinal analysis,Bellman equation,Ordinal regression,Mathematics
Journal
Volume
Issue
ISSN
191
2
0377-2217
Citations 
PageRank 
References 
165
6.72
10
Authors
3
Search Limit
100165
Name
Order
Citations
PageRank
Salvatore Greco13977266.79
Vincent Mousseau280850.52
Roman Slowinski35561516.06