Axiomatizations of the discrete Choquet integral and extensions

DOI

10.2991/eusflat.2011.149How to use a DOI?

Keywords

Aggregation function, discrete Choquet integral, discrete symmetric Choquet integral, Lovász extension, functional equation, Cauchy equation, comonotonic additivity, horizontal additivity

Abstract

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 medianadditivity, 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.

Copyright

© 2011, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

TY  - CONF
AU  - Miguel Couceiro
AU  - Jean-Luc Marichal
PY  - 2011/08
DA  - 2011/08
TI  - Axiomatizations of the discrete Choquet integral and extensions
BT  - Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)
PB  - Atlantis Press
SP  - 830
EP  - 835
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2011.149
DO  - 10.2991/eusflat.2011.149
ID  - Couceiro2011/08
ER  -