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Sugeno Integrals and the Commutation Problem

  • Didier Dubois
  • Hélène Fargier
  • Agnès Rico
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11144)

Abstract

In decision problems involving two dimensions (like several agents and several criteria) the properties of expected utility ensure that the result of a multicriteria multiperson evaluation does not depend on the order with which the aggregations of local evaluations are performed (agents first, criteria next, or the converse). We say that the aggregations on each dimension commute. Ben Amor, Essghaier and Fargier have shown that this property holds when using pessimistic possibilistic integrals on each dimension, or optimistic ones, while it fails when using a pessimistic possibilistic integral on one dimension and an optimistic one on the other. This paper studies and completely solves this problem when Sugeno integrals are used in place of possibilistic integrals, indicating that there are capacities other than possibility and necessity measures that ensure commutation of Sugeno integrals.

Keywords

Capacities Sugeno integrals Possibility theory Commutation 

Notes

Acknowledgements

This work is supported by ANR-11-LABX-0040-CIMI (Centre International de Mathématiques et d’Informatique) within the program ANR-11-IDEX-0002-02, project ISIPA.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.IRIT, Université Paul SabatierToulouse Cedex 9France
  2. 2.ERIC, Université Claude Bernard Lyon 1VilleurbanneFrance

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