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On Preference Representation on an Ordinal Scale

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Book cover Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2143))

Abstract

We present in this paper an attempt to deal with ordinal information in a strict ordinal framework. We address the problem of ranking alternatives in a multiple criteria decision making problem by the use of a compensatory aggregation operator, where scores are given on a finite ordinal scale. Necessary and sufficient conditions for the existence of a representation are given.

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References

  1. M. Grabisch, S.A. Orlovski, and R.R. Yager. Fuzzy aggregation of numerical preferences. In R. Slowiński, editor, Fuzzy Sets in Decision Analysis, Operations Research and Statistics, The Handbooks of Fuzzy Sets Series, D. Dubois and H. Prade (eds), pages 31–68. Kluwer Academic, 1998.

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  2. M. Grabisch and M. Roubens. Probabilistic interactions among players of a cooperative game. In M.J. Machina and B. Munier, editors, Beliefs, Interactions and Preferences. Kluwer Academic, 1999.

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  3. F.S. Roberts. Measurement Theory. Addison-Wesley, 1979.

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  4. M. Sugeno. Theory of fuzzy integrals and its applications. PhD thesis, Tokyo Institute of Technology, 1974.

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  5. P.F. Velleman and L. Wilkinson. Nominal, ordinal, interval, and ratio typologies are misleading. The American Statistician, 47(1):65–72, 1993.

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Author information

Author notes

  1. Michel Grabisch

    Present address: THALES, Corporate Research Laboratory, Domaine de Corbeville, Orsay, France

Authors and Affiliations

  1. LIP6, UPMC 8, rue du Capitaine Scott, 75015, Paris, France

    Michel Grabisch

Authors
  1. Michel Grabisch
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Editor information

Editors and Affiliations

  1. Université Paul Sabatier, IRIT-CNRS, 118 route de Narbonne, 31062, Toulouse Cedex 4, France

    Salem Benferhat  & Philippe Besnard  & 

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© 2001 Springer-Verlag Berlin Heidelberg

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Grabisch, M. (2001). On Preference Representation on an Ordinal Scale. In: Benferhat, S., Besnard, P. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2001. Lecture Notes in Computer Science(), vol 2143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44652-4_4

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  • DOI: https://doi.org/10.1007/3-540-44652-4_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42464-2

  • Online ISBN: 978-3-540-44652-1

  • eBook Packages: Springer Book Archive

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