Choquet Integrals and OWA Criteria as a Natural (and Optimal) Next Step After Linear Aggregation: A New General Justification

Authors

Francois Modave
Martine Ceberio, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

8-2008

Comments

Technical Report: UTEP-CS-08-28a

To appear in Alexander Gelbukh and Eduardo F. Morales (eds.), Proceedings of the 7th Mexican International Conference on Artificial Intelligence MICAI'08, Mexico City, Mexico, October 27-31, 2008, Springer Lecture Notes on Artificial Intelligence, 2008, Vol. 5317, pp. 741-753.

Abstract

In multi-criteria decision making, it is necessary to aggregate (combine) utility values corresponding to several criteria (parameters). The simplest way to combine these values is to use linear aggregation. In many practical situations, however, linear aggregation does not fully adequately describe the actual decision making process, so non-linear aggregation is needed.

From the purely mathematical viewpoint, the next natural step after linear functions is the use of quadratic functions. However, in decision making, a different type of non-linearities are usually more adequate than quadratic ones: non-linearities like OWA or Choquet integral that use min and max in addition to linear combinations. In this paper, we explain the empirically observed advantage of such aggregation operations.