Axiomatizations of Lovász extensions of pseudo-Boolean functions
Marichal, Jean-Luc; Couceiro, Miguel (2012), Axiomatizations of Lovász extensions of pseudo-Boolean functions, Fuzzy Sets and Systems, 181, 1, p. 28–38. http://dx.doi.org/10.1016/j.fss.2011.05.006
TypeArticle accepté pour publication ou publié
Journal nameFuzzy Sets and Systems
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, these 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.
Subjects / KeywordsFunctional equation; Lovász extension; Discrete symmetric Choquet integral; Discrete Choquet integral; Aggregation function
Showing items related by title and author.