Axiomatizations of the discrete Choquet integral and extensions
Marichal, Jean-Luc; Couceiro, Miguel (2011), Axiomatizations of the discrete Choquet integral and extensions, in Mauris, G.; Montero, J.; Galichet, S., Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011) et les rencontres francophones sur la Logique Floue et ses Applications (LFA-2011), Aix-les-Bains, France, July 18-22, 2011., European Society for Fuzzy Logic and Technology
TypeCommunication / Conférence
Conference titleEUSFLAT/LFA 2011
Conference cityAix les Bains
Book titleProceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011) et les rencontres francophones sur la Logique Floue et ses Applications (LFA-2011), Aix-les-Bains, France, July 18-22, 2011.
Book authorMauris, G.; Montero, J.; Galichet, S.
Number of pages1097 p.
MetadataShow full item record
Abstract (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 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.
Subjects / Keywordshorizontal additivity; comonotonic additivity; Cauchy equation; functional equation; Lovász extension; iscrete symmetric Choquet integral; discrete Choquet integral; Aggregation function
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