Discrete Integrals Based on Comonotonic Modularity

Axioms

Miguel Couceiro¹ 

[1] Lamsade, University Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, Paris Cedex 16 F-75775, France; E-Mail:

关键词: aggregation function;    discrete Choquet integral;    discrete Sugeno integral;    functional equation;    comonotonic additivity;    comonotonic modularity;    axiomatization;   

DOI  :  10.3390/axioms2030390

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.