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Constructing Preference Relations from Utilities and Vice Versa

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 611))

Abstract

In decision making, the suitability of decision options may be specified by utility values for each option or by preference values for each pair of options. This paper introduces a new approach to construct a matrix of pairwise preference values from a vector of utility values, which is called the U2P transformation. The U2P transformation satisfies reciprocity, triangle condition, weak transitivity, restricted max–min transitivity, and restricted max–max transitivity, but it violates (unrestricted) max–min transitivity, (unrestricted) max–max transitivity, multiplicative transitivity, and additive transitivity. Inversion of the U2P transformation yields the P2U transformation which can be used to construct a vector of utility values from a matrix of pairwise preference values. Numerical experiments with movie ratings illustrate the practical use of the U2P and P2U transformations.

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Author information

Authors and Affiliations

  1. Siemens AG, Corporate Technology, Otto–Hahn–Ring 6, 81739, Munich, Germany

    Thomas A. Runkler

Authors
  1. Thomas A. Runkler
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Correspondence to Thomas A. Runkler .

Editor information

Editors and Affiliations

  1. INESC-ID,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Joao Paulo Carvalho

  2. LIP 6, Université Pierre et Marie Curie, Paris, France

    Marie-Jeanne Lesot

  3. School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Uzay Kaymak

  4. IDMEC,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Susana Vieira

  5. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  6. Iona College, Machine Intelligence Institute, New Rochelle, New York, USA

    Ronald R. Yager

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© 2016 Springer International Publishing Switzerland

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Runkler, T.A. (2016). Constructing Preference Relations from Utilities and Vice Versa. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 611. Springer, Cham. https://doi.org/10.1007/978-3-319-40581-0_44

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  • DOI: https://doi.org/10.1007/978-3-319-40581-0_44

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40580-3

  • Online ISBN: 978-3-319-40581-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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