Cluster Decomposition of the Body of Evidence | SpringerLink
Skip to main content

Cluster Decomposition of the Body of Evidence

  • Conference paper
  • First Online:
Belief Functions: Theory and Applications (BELIEF 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13506))

Included in the following conference series:

  • 471 Accesses

Abstract

Two algorithms for the body of evidence clustering are developed and studied in this paper. The first algorithm is based on the use of the distribution density function of conflicting focal elements of the body of evidence. The second algorithm is similar to the k-means algorithm, but it uses the external conflict measure instead of the metric. It is shown that cluster decomposition can be used to evaluate the internal conflict of the body of evidence.

The financial support from the Government of the Russian Federation within the framework of the implementation of the 5–100 Programme Roadmap of the National Research University Higher School of Economics is acknowledged.

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

Access this chapter

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 5719
Price includes VAT (Japan)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 7149
Price includes VAT (Japan)
  • 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. Bronevich, A., Lepskiy, A.: Imprecision indices: axiomatic, properties and applications. Int. J. Gen Syst 44(7–8), 812–832 (2015)

    Article  MathSciNet  Google Scholar 

  2. Bronevich, A., Lepskiy, A.: Measures of conflict, basic axioms and their application to the clusterization of a body of evidence. Fuzzy Sets Syst. 446, 277–300 (2021). https://doi.org/10.1016/j.fss.2021.04.016

    Article  MathSciNet  Google Scholar 

  3. Daniel, M.: Properties of plausibility conflict of belief functions. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013. LNCS (LNAI), vol. 7894, pp. 235–246. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38658-9_22

    Chapter  Google Scholar 

  4. Dempster, A.P.: Upper and lower probabilities induced by multivalued mapping. Ann. Math. Stat. 38, 325–339 (1967)

    Article  MathSciNet  Google Scholar 

  5. Denœux, T.: Inner and outer approximation of belief structures using a hierarchical clustering approach. Int. J. Uncertainty Fuzziness Knowl.-Based Syst. 9(4), 437–460 (2001)

    Google Scholar 

  6. Harmanec, D.: Faithful approximations of belief functions. In: Laskey, K.B., Prade, H. (eds.) Uncertainty in Artificial Intelligence 15 (UAI 1999), Stockholm, Sweden (1999)

    Google Scholar 

  7. Jousselme, A.-L., Maupin, P.: Distances in evidence theory: comprehensive survey and generalizations. Int. J. Approx. Reason. 53, 118–145 (2012)

    Article  MathSciNet  Google Scholar 

  8. Lepskiy, A.: Analysis of information inconsistency in belief function theory. Part I: external conflict. Control Sci. 5, 2–16 (2021)

    Google Scholar 

  9. Lepskiy, A.: Analysis of information inconsistency in belief function theory. Part II: internal conflict. Control Sci. 6, 2–12 (2021)

    Google Scholar 

  10. Petit-Renaud, S., Denœux, T.: Handling different forms of uncertainty in regression analysis: a fuzzy belief structure approach. In: Hunter, A., Parsons, S. (eds.) ECSQARU 1999. LNCS (LNAI), vol. 1638, pp. 340–351. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48747-6_31

    Chapter  Google Scholar 

  11. Pichon, F., Jousselme, A.L., Abdallah, N.B.: Several shades of conflict. Fuzzy Sets Syst. 366, 63–84 (2019)

    Article  MathSciNet  Google Scholar 

  12. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    Book  Google Scholar 

  13. Yager, R.: On the Dempster-Shafer framework and new combination rules. Inf. Sci. 41, 93–137 (1987)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alexander Lepskiy .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Lepskiy, A. (2022). Cluster Decomposition of the Body of Evidence. In: Le Hégarat-Mascle, S., Bloch, I., Aldea, E. (eds) Belief Functions: Theory and Applications. BELIEF 2022. Lecture Notes in Computer Science(), vol 13506. Springer, Cham. https://doi.org/10.1007/978-3-031-17801-6_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-17801-6_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-17800-9

  • Online ISBN: 978-3-031-17801-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics