[en] Recent - and less recent - work has been devoted to learning additive value functions or a Choquet capacity
to represent the preference of a decision maker on a set of alternatives described by their performance on
the relevant attributes. In this work we compare the ability of related models to represent rankings of such
alternatives. Our experiments are designed as follows. We generate a number of alternatives by drawing at
random a vector of evaluations for each of them. We then draw a random order on these alternatives and we
examine whether this order is representable by a simple weighted sum, a Choquet integral with respect to a
2- or 3-additive capacity, an additive value function in general or a piecewise-linear additive value function
with 2 or 3 pieces. We also generate non preferentially independent data in order to test to which extent 2-
or 3-additive Choquet integrals allow to represent the given orders. The results explore how representability
depends on varying the numbers of alternatives and criteria.
Research center :
CRTI - Centre de Recherche en Technologie de l'Information
Disciplines :
Quantitative methods in economics & management Mathematics
Author, co-author :
Meyer, Patrick
Pirlot, Marc ; Université de Mons > Faculté Polytechnique > Mathématique et Recherche opérationnelle
Language :
English
Title :
On the expressiveness of the additive value function and the Choquet integral models
Publication date :
15 November 2012
Event name :
From Multiple Criteria Decision Aid to Preference Learning DA2PL 2012
Event place :
Mons, Belgium
Event date :
2012
Research unit :
F151 - Mathématique et Recherche opérationnelle
Research institute :
R300 - Institut de Recherche en Technologies de l'Information et Sciences de l'Informatique
