• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • LAMSADE (UMR CNRS 7243)
  • LAMSADE : Publications
  • View Item
  •   BIRD Home
  • LAMSADE (UMR CNRS 7243)
  • LAMSADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail - Request a copy

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

Type
Article accepté pour publication ou publié
Date
2012-09-27
Journal name
Fuzzy Sets and Systems
Volume
181
Number
1
Publisher
Elsevier
Pages
28–38
Publication identifier
http://dx.doi.org/10.1016/j.fss.2011.05.006
Metadata
Show full item record
Author(s)
Marichal, Jean-Luc
Couceiro, Miguel
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 / Keywords
Functional equation; Lovász extension; Discrete symmetric Choquet integral; Discrete Choquet integral; Aggregation function

Related items

Showing items related by title and author.

  • Thumbnail
    Axiomatizations of quasi-Lovász extensions of pseudo-Boolean functions 
    Marichal, Jean-Luc; Couceiro, Miguel (2011) Article accepté pour publication ou publié
  • Thumbnail
    Hierarchies of local monotonicities and lattice derivatives for Boolean and pseudo-Boolean functions 
    Waldhauser, Tamás; Marichal, Jean-Luc; Couceiro, Miguel (2012) Communication / Conférence
  • Thumbnail
    Locally monotone Boolean and pseudo-Boolean functions 
    Waldhauser, Tamás; Marichal, Jean-Luc; Couceiro, Miguel (2012) Article accepté pour publication ou publié
  • Thumbnail
    Axiomatizations of the discrete Choquet integral and extensions 
    Marichal, Jean-Luc; Couceiro, Miguel (2011) Communication / Conférence
  • Thumbnail
    The arity gap of order-preserving functions and extensions of pseudo-Boolean functions 
    Waldhauser, Tamás; Lehtonen, Erkko; Couceiro, Miguel (2012) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo