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Discrete Integrals Based on Comonotonic Modularity

Couceiro, Miguel; Marichal, Jean-Luc (2013), Discrete Integrals Based on Comonotonic Modularity, Axioms, 2, 3, p. 390-403. 10.3390/axioms2030390

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01090567
Date
2013
Journal name
Axioms
Volume
2
Number
3
Pages
390-403
Publication identifier
Metadata
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Author(s)
Couceiro, Miguel
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Marichal, Jean-Luc
Mathematics Research Unit
Abstract (EN)
It is known that several discrete integrals, including the Choquet and Sugeno integrals, as well as some of their generalizations, are comonotonically modular functions.Based on a recent description of the class of comonotonically modular functions, we axiomatically identify more general families of discrete integrals that are comonotonically modular, including signed Choquet integrals and symmetric signed Choquet integrals, as well as natural extensions of Sugeno integrals.
Subjects / Keywords
aggregation function; discrete Choquet integral; discrete Sugeno integral; functional equation; comonotonic additivity; comonotonic modularity; axiomatization