# On the Extension of Pseudo-Boolean Functions for the Aggregation of Interacting Criteria

1 SYSDEF - Systèmes d'aide à la décision et à la formation
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : The paper presents an analysis on the use of integrals defined for non-additive measures (or capacities) as the Choquet and the \Sipos{} integral, and the multilinear model, all seen as extensions of pseudo-Boolean functions, and used as a means to model interaction between criteria in a multicriteria decision making problem. The emphasis is put on the use, besides classical comparative information, of information about difference of attractiveness between acts, and on the existence, for each point of view, of a neutral level'', allowing to introduce the absolute notion of attractive or repulsive act. It is shown that in this case, the Sipos integral is a suitable solution, although not unique. Properties of the Sipos integral as a new way of aggregating criteria are shown, with emphasis on the interaction among criteria.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-00272780
Contributor : Michel Grabisch <>
Submitted on : Friday, April 11, 2008 - 5:42:14 PM
Last modification on : Thursday, July 2, 2020 - 12:48:01 PM
Document(s) archivé(s) le : Friday, May 21, 2010 - 1:40:52 AM

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### Identifiers

• HAL Id : hal-00272780, version 1
• ARXIV : 0804.1921

### Citation

Michel Grabisch, Christophe Labreuche, Jean-Claude Vansnick. On the Extension of Pseudo-Boolean Functions for the Aggregation of Interacting Criteria. European Journal of Operational Research, Elsevier, 2003, 148, pp.28-47. ⟨hal-00272780⟩

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