Skip to main content
SpringerLink
Log in

The d-Interaction Index in MCDA

  • 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))

  • 674 Accesses

Abstract

In the context of the representation of a preference information, we introduce a new interaction index based on a distance, in order to better model the interactions among criteria. This index, which provides robust interpretations of the interactions, is directly related to the independence property required when an additive model is used as an aggregation function.

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

References

  1. Bouyssou, D., Marchant, T., Pirlot, M., Perny, P., Tsoukiàs, A., Vincke, P.: Evaluation and Decision Models: A Critical Perspective. Kluwer Academic, Dordrecht (2000)

    Book  Google Scholar 

  2. Bouyssou, D., Marchant, T., Pirlot, M., Tsoukiàs, A., Vincke, P.: Evaluation and decision models with multiple criteria: stepping stones for the analyst. In: International Series in Operations Research and Management Science, vol. 86. Boston, 1st edn. (2006)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  4. Dyer, J.S.: MAUT - multiattribute utility theory. In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multiple Criteria Decision Analysis: State of the Art Surveys, pp. 265–285. Springer Verlag, Boston, Dordrecht, London (2005). https://doi.org/10.1007/0-387-23081-5_7

    Chapter  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  6. Grabisch, M., Labreuche, Ch.: A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. 4OR 6, 1–44 (2008)

    Google Scholar 

  7. Grabisch, M., Labreuche, C.: Fuzzy measures and integrals in MCDA. In: Multiple Criteria Decision Analysis: State of the Art Surveys. ISORMS, vol. 78, pp. 563–604. Springer, New York (2005). https://doi.org/10.1007/0-387-23081-5_14

    Chapter  Google Scholar 

  8. Kendall, M.G.: A new measure of rank correlation. Biometrika 30(1/2), 81–93 (1938)

    Article  Google Scholar 

  9. Mayag, B., Grabisch, M., Labreuche, C.: A characterization of the 2-additive Choquet integral through cardinal information. Fuzzy Sets Syst. 184(1), 84–105 (2011)

    Article  MathSciNet  Google Scholar 

  10. Mayag, B., Grabisch, M., Labreuche, C.: A representation of preferences by the Choquet integral with respect to a 2-additive capacity. Theory Dec. 71(3), 297–324 (2011)

    Article  MathSciNet  Google Scholar 

  11. Mayag, B., Bouyssou, D.: Necessary and possible interaction between criteria in a 2-additive choquet integral model. Eur. J. Oper. Res. 283(1), 308–320 (2020)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  13. Shapley, L.S.: A value for \(n\)-person games. In: Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games, Vol. II, number 28 in Annals of Mathematics Studies, pp. 307–317. Princeton University Press (1953)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University Paris-Dauphine, PSL Research university, LAMSADE, CNRS, UMR 7243, Place du Maréchal de Lattre de Tassigny, 75775, Paris cedex 16, France

    Brice Mayag

  2. Ecole Normale Supérieure de Yaoundé, MASS Laboratory, BP 47, Yaoundé, Cameroon

    Bertrand Tchantcho

Authors
  1. Brice Mayag
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bertrand Tchantcho
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Brice Mayag .

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

Mayag, B., Tchantcho, B. (2022). The d-Interaction Index in MCDA. 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_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-08974-9_17

  • 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