Reference : Quasi-Lovász extensions and their symmetric counterparts
 Document type : Scientific congresses, symposiums and conference proceedings : Paper published in a book Discipline(s) : Physical, chemical, mathematical & earth Sciences : MathematicsBusiness & economic sciences : Quantitative methods in economics & management To cite this reference: http://hdl.handle.net/10993/9592
 Title : Quasi-Lovász extensions and their symmetric counterparts Language : English Author, co-author : Couceiro, Miguel [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Marichal, Jean-Luc [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Publication date : 2012 Main document title : 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 Editor : Greco, S. Bouchon-Meunier, B. Coletti, G. Fedrizzi, M. Matarazzo, B. Yager, R. R. Publisher : Springer Collection and collection volume : Communications in Computer and Information Science, Vol. 300 Pages : 178-187 Peer reviewed : Yes On invitation : No Audience : International ISBN : 978-3-642-31723-1 City : Heidelberg Country : Germany Event name : 14th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2012) Event date : from 09-07-2012 to 13-07-2012 Event place (city) : Catania Event country : Italy Keywords : [en] Aggregation function ; discrete Choquet integral ; Lovász extension ; comonotonic modularity ; invariance under horizontal differences Abstract : [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. Funders : University of Luxembourg - UL Name of the research project : F1R-MTH-PUL-12RDO2 > MRDO2 > 01/02/2012 - 31/01/2015 > MARICHAL Jean-Luc Target : Researchers ; Professionals ; Students Permalink : http://hdl.handle.net/10993/9592 Other URL : http://www.ipmu2012.unict.it/index.html

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