Skip to main content
SpringerLink
Log in

Study of the Instability of the Sign of the Nonadditivity Index in a Choquet Integral Model

  • Conference paper
  • First Online:
Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1602))

Abstract

This paper studies the instability of the sign of the nonadditivity index between criteria in a Choquet integral model. Nonadditivity is an essential property of capacities defined on the sets of decision criteria and allows one to flexibly represent the phenomenon of interaction between criteria. In some cases, we show that the sign of the nonadditivity index proposed in the literature depends on arbitrary choice of a numerical representation in the set of all numerical representations compatible with the strict preferential information given by the Decision Maker(DM). This makes its interpretation difficult. We illustrate our results with examples.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Similar content being viewed by others

References

  1. Bouyssou, D., Pirlot, M.: Conjoint measurement tools for MCDM. In: Greco, S., Ehrgott, M., Figueira, J.R. (eds.) Multiple Criteria Decision Analysis. ISORMS, vol. 233, pp. 97–151. Springer, New York (2016). https://doi.org/10.1007/978-1-4939-3094-4_4

    Chapter  Google Scholar 

  2. Choquet, G.: Theory of capacities. Annales de l’Institut Fourier 5, 131–295 (1954)

    Article  MathSciNet  Google Scholar 

  3. Fujimoto, K.: Cardinal-probabilistic interaction indices and their applications: a survey. J. Adv. Comput. Intell. Intell. Inform. 7(2), 79–85 (2003)

    Article  Google Scholar 

  4. Gondran, M., Minoux, M.: Graphes et algorithmes, 3e édition. Eyrolles, Paris (1995)

    Google Scholar 

  5. Grabisch, M.: Fuzzy integral in multicriteria decision making. Fuzzy Sets Syst. 69(3), 279–298 (1995)

    Article  MathSciNet  Google Scholar 

  6. Grabisch, M.: The application of fuzzy integrals in multicriteria decision making. Eur. J. Oper. Res. 89(3), 445–456 (1996)

    Article  MathSciNet  Google Scholar 

  7. Grabisch, M.: \(k\)-Order additive discrete fuzzy measures and their representation. Fuzzy Sets Syst. 92(2), 167–189 (1997)

    Article  MathSciNet  Google Scholar 

  8. Grabisch, M.: Set Functions, Games and Capacities in Decision Making. Theory and Decision Library C, vol. 46. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-30690-2

  9. Grabisch, M., Labreuche, C.: Fuzzy measures and integrals in MCDA. In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multiple Criteria Decision Analysis. State of the art surveys, number 142 in International Series in Operations Research & Management Science, pp. 563–608. Springer, Berlin (2005)

    Google Scholar 

  10. Grabisch, M., Labreuche, C.: A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. Ann. Oper. Res. 175(1), 247–290 (2010)

    Article  MathSciNet  Google Scholar 

  11. Grabisch, M., Labreuche, C., Vansnick, J.-C.: On the extension of pseudo-Boolean functions for the aggregation of interacting criteria. Eur. J. Oper. Res. 148, 28–47 (2003)

    Article  MathSciNet  Google Scholar 

  12. Kaldjob Kaldjob, P.A., Mayag, B., Bouyssou, D.: Necessary and possible interaction between criteria in a general Choquet integral model. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems, pp. 457–466 (2020)

    Google Scholar 

  13. Lidl, R., Pilz, G.: Applied Abstract Algebra. Springer, New York (1984). https://doi.org/10.1007/978-1-4615-6465-2

    Book  MATH  Google Scholar 

  14. Mayag, B., Bouyssou, D.: Necessary and possible interaction between criteria in a 2-additive Choquet integral model. Eur. J. Oper. Res. 283, 308–320 (2019)

    Article  MathSciNet  Google Scholar 

  15. Wu, J.Z., Beliakov, G.: Nonadditivity index and capacity identification method in the context of multicriteria decision making. Inf. Sci. 467, 398–406 (2018)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University Paris-Dauphine, University PSL, CNRS, LAMSADE, 75016, Paris, France

    Paul Alain Kaldjob Kaldjob, Brice Mayag & Denis Bouyssou

Authors
  1. Paul Alain Kaldjob Kaldjob
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Brice Mayag
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Denis Bouyssou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paul Alain Kaldjob Kaldjob .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

  2. University of Oviedo, Oviedo, Spain

    Inés Couso

  3. University of Cádiz, Cádiz, Spain

    Jesús Medina

  4. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. University of Perugia, Perugia, Italy

    Davide Petturiti

  6. Sorbonne Université, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, NY, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kaldjob Kaldjob, P.A., Mayag, B., Bouyssou, D. (2022). Study of the Instability of the Sign of the Nonadditivity Index in a Choquet Integral Model. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1602. Springer, Cham. https://doi.org/10.1007/978-3-031-08974-9_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-08974-9_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-08973-2

  • Online ISBN: 978-3-031-08974-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation