Skip to main content
SpringerLink
Log in

An Axiomatization of the Choquet Integral and Its Utility Functions without Any Commensurability Assumption

  • Conference paper
Advances in Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 300))

Abstract

We propose an axiomatization of global utility functions that can be factorized as a composition of a Choquet integral with local utility functions, without assuming any commensurability condition. This was an open problem in the literature. The main axiom, called Commensurability Through Interaction (CTI), allows to construct commensurate sequences and by consequence, the utility functions, thanks to the presence of interaction between criteria.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Schmeidler, D.: Integral representation without additivity. Proc. of the Amer. Math. Soc. 97(2), 255–261 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  2. Benvenuti, P., Mesiar, R., Vivona, D.: Monotone set functions-based integrals. In: Pap, E. (ed.) Handbook of Measure Theory, pp. 1329–1379. Elsevier Science (2002)

    Google Scholar 

  3. Couceiro, M., Marichal, J.: Axiomatizations of lovász extensions of pseudo-Boolean functions. Fuzzy Sets and Systems 181, 28–38 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Marichal, J.L.: An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria. IEEE Tr. on Fuzzy Systems 8(6), 800–807 (2000)

    Article  MathSciNet  Google Scholar 

  5. Schmeidler, D.: Subjective probability and expected utility without additivity. Econometrica 57(3), 571–587 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  6. Couceiro, M., Marichal, J.: Axiomatizations of quasi-lovász extensions of pseudo-Boolean functions. Aequationes Mathematicae 82, 213–231 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Grabisch, M., Murofushi, T., Sugeno, M.: Fuzzy Measures and Integrals. Theory and Applications (edited volume). STUDFUZZ. Physica Verlag (2000)

    Google Scholar 

  8. Choquet, G.: Theory of capacities. Annales de l’Institut Fourier 5, 131–295 (1953)

    Article  MathSciNet  Google Scholar 

  9. Murofushi, T., Soneda, S.: Techniques for reading fuzzy measures (III): interaction index. In: 9th Fuzzy System Symposium, Sapporo, Japan, pp. 693–696 (May 1993)

    Google Scholar 

  10. Labreuche, C., Grabisch, M.: The Choquet integral for the aggregation of interval scales in multicriteria decision making. Fuzzy Sets & Systems 137, 11–26 (2003)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Thales Research & Technology, 1 avenue Augustin Fresnel, 91767, Palaiseau Cedex, France

    Christophe Labreuche

Authors
  1. Christophe Labreuche
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. CNRS UMR 7606, DAPA, LIP6 8, Université Pierre et Marie Curie - Paris6, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute — IONA College,, 10801, New Rochelle, NY, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Labreuche, C. (2012). An Axiomatization of the Choquet Integral and Its Utility Functions without Any Commensurability Assumption. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31724-8_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31723-1

  • Online ISBN: 978-3-642-31724-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation