title: |
Axiomatizations of the discrete Choquet integral and extensions |
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publication: |
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part of series: |
Advances in Intelligent Systems Research | |
| pages: | 830 - 835 | |
DOI: |
To be assigned soon (how to use a DOI) | |
author(s): |
Miguel Couceiro, Jean-Luc Marichal, Joao Paulo Carvalho, Jorgi Inglada |
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publication date: |
July 2011 |
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keywords: |
Aggregation function, discrete Choquet integral, discrete symmetric Choquet integral, Lovász extension, functional equation, Cauchy equation, comonotonic additivity, horizontal additivity |
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abstract: |
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, the
latter 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 medianadditivity,
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.
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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |