Axiomatizations of the discrete Choquet integral and extensions
Miguel Couceiro, Jean-Luc Marichal
Available Online August 2011.
- https://doi.org/10.2991/eusflat.2011.149How to use a DOI?
- Aggregation function, discrete Choquet integral, discrete symmetric Choquet integral, Lovász extension, functional equation, Cauchy equation, comonotonic additivity, horizontal additivity
- 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.
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
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 PB - Atlantis Press SP - 830 EP - 835 SN - 1951-6851 UR - https://doi.org/10.2991/eusflat.2011.149 DO - https://doi.org/10.2991/eusflat.2011.149 ID - Couceiro2011/08 ER -