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Axioms 2013, 2(3), 390-403; doi:10.3390/axioms2030390
Article

Discrete Integrals Based on Comonotonic Modularity

1
 and
2,*
Received: 16 April 2013 / Revised: 31 May 2013 / Accepted: 19 June 2013 / Published: 23 July 2013
(This article belongs to the Special Issue Axiomatic Approach to Monotone Measures and Integrals)
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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 aggregation function; discrete Choquet integral; discrete Sugeno integral; functional equation; comonotonic additivity; comonotonic modularity; axiomatization
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Couceiro, M.; Marichal, J.-L. Discrete Integrals Based on Comonotonic Modularity. Axioms 2013, 2, 390-403.

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