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 [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 >] | |

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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