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Discrete Integrals Based on Comonotonic Modularity
Lamsade, University Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, Paris Cedex 16 F-75775, France
Mathematics Research Unit, University of Luxembourg, 6 Rue Coudenhove-Kalergi, Luxembourg L-1359, Luxembourg
* Author to whom correspondence should be addressed.
Received: 16 April 2013; in revised form: 31 May 2013 / Accepted: 19 June 2013 / Published: 23 July 2013
Abstract: 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.
Keywords: aggregation function; discrete Choquet integral; discrete Sugeno integral; functional equation; comonotonic additivity; comonotonic modularity; axiomatization
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MDPI and ACS Style
Couceiro, M.; Marichal, J.-L. Discrete Integrals Based on Comonotonic Modularity. Axioms 2013, 2, 390-403.
Couceiro M, Marichal J-L. Discrete Integrals Based on Comonotonic Modularity. Axioms. 2013; 2(3):390-403.
Couceiro, Miguel; Marichal, Jean-Luc. 2013. "Discrete Integrals Based on Comonotonic Modularity." Axioms 2, no. 3: 390-403.