Reference : Axiomatizations of the discrete Choquet integral and extensions
Scientific congresses, symposiums and conference proceedings : Paper published in a book
Physical, chemical, mathematical & earth Sciences : Mathematics
Business & economic sciences : Quantitative methods in economics & management
http://hdl.handle.net/10993/9512
Axiomatizations of the discrete Choquet integral and extensions
English
Couceiro, Miguel mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2011
Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011) and LFA-2011
Galichet, Sylvie
Montero, Javier
Mauris, Gilles
Atlantis Press
830-835
Yes
No
International
978-90-78677-00-0
Joint 7th Conference of the European Society for Fuzzy Logic and Technology and the 17th Rencontres Francophones sur la Logique Floue et ses Applications (2011 EUSFLAT-LFA Joint Conference)
from 18-07-2011 to 22-07-2011
Aix-les-Bains
France
[en] aggregation function ; discrete Choquet integral ; discrete symmetric Choquet integral ; Lovász extension ; functional equation ; Cauchy equation ; comonotonic additivity ; horizontal additivity
[en] Three important properties in aggregation theory are investigated, namely horizontal min-additivity, horizontal max-additivity, and comonotonic additivity, which are defined by certain relaxations of the Cauchy functional equation in several variables. We show that these properties are equivalent and we completely describe the functions characterized by them. By adding some regularity conditions, the latter functions coincide with the Lovász extensions vanishing at the origin, which subsume the discrete Choquet integrals. We also propose a simultaneous generalization of horizontal min-additivity and horizontal max-additivity, called horizontal median-additivity, and we describe the corresponding function class. Additional conditions then reduce this class to that of symmetric Lovász extensions, which includes the discrete symmetric Choquet integrals.
University of Luxembourg - UL
F1R-MTH-PUL-09MRDO > MRDO > 01/01/2009 - 31/12/2011 > MARICHAL Jean-Luc
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/9512
http://www.atlantis-press.com/publications/aisr/eusflat-11/

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