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Quasi-Lovász Extensions on Bounded Chains

  • Conference paper
Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 442))

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Abstract

We study quasi-Lovász extensions as mappings defined on a nonempty bounded chain C, and which can be factorized as f(x 1,…,x n ) = L(ϕ(x 1),…,ϕ(x n )), where L is the Lovász extension of a pseudo-Boolean function and is an order-preserving function.

We axiomatize these mappings by natural extensions to properties considered in the authors’ previous work. Our motivation is rooted in decision making under uncertainty: such quasi-Lovász extensions subsume overall preference functionals associated with discrete Choquet integrals whose variables take values on an ordinal scale C and are transformed by a given utility function .

Furthermore, we make some remarks on possible lattice-based variants and bipolar extensions to be considered in an upcoming contribution by the authors.

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Author information

Authors and Affiliations

  1. LAMSADE - CNRS, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Miguel Couceiro

  2. Mathematics Research Unit, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, L–1359, Luxembourg, G.-D., Luxembourg

    Jean-Luc Marichal

Authors
  1. Miguel Couceiro
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  2. Jean-Luc Marichal
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Editor information

Editors and Affiliations

  1. University Montpellier 2, LIRMM - CNRS UMR 5506, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Anne Laurent

  2. LIRMM, UMR CNRS/Universite Montpellier II, 161 rue Ada, 34392, Montpellier cedex 5, France

    Olivier Strauss

  3. LIP6, UPMC Univ. Paris 06, CNRS UMR 7606, F-75005, Paris, France

    Bernadette Bouchon-Meunier

  4. Dept. of Information Systems, Iona College, 710 North Ave, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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Couceiro, M., Marichal, JL. (2014). Quasi-Lovász Extensions on Bounded Chains. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 442. Springer, Cham. https://doi.org/10.1007/978-3-319-08795-5_21

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  • DOI: https://doi.org/10.1007/978-3-319-08795-5_21

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08794-8

  • Online ISBN: 978-3-319-08795-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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