Reference : Quasi-Lovász extensions and their symmetric counterparts
Scientific congresses, symposiums and conference proceedings : Paper published in a book
Physical, chemical, mathematical & earth Sciences : Mathematics
Business & economic sciences : Quantitative methods in economics & management
http://hdl.handle.net/10993/9592
Quasi-Lovász extensions and their symmetric counterparts
English
Couceiro, Miguel mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2012
Advances on Computational Intelligence, Part IV, 14th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, Catania, Italy, July 9-13, 2012, Proceedings, Part IV
Greco, S.
Bouchon-Meunier, B.
Coletti, G.
Fedrizzi, M.
Matarazzo, B.
Yager, R. R.
Springer
Communications in Computer and Information Science, Vol. 300
178-187
Yes
No
International
978-3-642-31723-1
Heidelberg
Germany
14th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2012)
from 09-07-2012 to 13-07-2012
Catania
Italy
[en] Aggregation function ; discrete Choquet integral ; Lovász extension ; comonotonic modularity ; invariance under horizontal differences
[en] We introduce the concept of quasi-Lov\'asz extension as being a mapping $f\colon I^n\to\R$ defined over a nonempty real interval $I$ containing the origin, and which can be factorized
as $f(x_1,\ldots,x_n)=L(\varphi(x_1),\ldots,\varphi(x_n))$, where $L$ is the Lov\'asz extension of a pseudo-Boolean function $\psi\colon\{0,1\}^n\to\R$ (i.e., the function $L\colon\R^n\to\R$ whose restriction to each simplex of the standard triangulation of $[0,1]^n$ is the unique affine function which agrees with $\psi$ at the vertices of this simplex) and $\varphi\colon I\to\R$ is a nondecreasing function vanishing at the origin. These functions appear naturally within the scope of decision making under uncertainty since they subsume overall preference functionals associated with discrete Choquet integrals whose variables are transformed by a given utility function.

To axiomatize the class of quasi-Lov\'asz extensions, we propose generalizations of properties used to characterize the Lov\'asz extensions, including a comonotonic version of modularity and a natural relaxation of homogeneity. A variant of the latter property enables us to axiomatize also the class of symmetric quasi-Lov\'asz extensions, which are compositions
of symmetric Lov\'asz extensions with $1$-place nondecreasing odd functions.
University of Luxembourg - UL
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/9592
http://www.ipmu2012.unict.it/index.html

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