Reference : On three properties of the discrete Choquet integral

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/10993/9516

On three properties of the discrete Choquet integral

English

Couceiro, Miguel[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]

Marichal, Jean-Luc[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

2011

32nd Linz Seminar on Fuzzy Set Theory (LINZ 2011) - Decision Theory: Qualitative and Quantitative Approaches

Dubois, Didier

Grabisch, Michel

Mesiar, Radko

Klement, Erich Peter

29-32

Yes

No

International

32nd Linz Seminar on Fuzzy Set Theory (LINZ 2011)

from 01-02-2011 to 05-02-2011

Erich Peter Klement (Chairman), Johannes Kepler University Linz

Linz

Austria

[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, these functions coincide with the LovĂˇsz extensions vanishing at the origin, which subsume the discrete Choquet integrals.