Skip to main content
SpringerLink
Log in

Properties of Plausibility Conflict of Belief Functions

  • Conference paper
Book cover Artificial Intelligence and Soft Computing (ICAISC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7894))

Included in the following conference series:

Abstract

This theoretical contribution studies mathematical properties of plausibility conflict of belief functions. The analysis is performed for belief functions defined on 2-element frames, then the results are generalized to general finite frames. After that, an analogous analysis of Liu’s degree of conflict is presented, to enable its comparison to the plausibility conflict. To be more efficient, a simplification of formula and computation of Liu’s degree of conflict is suggested.

A series of examples and graphical demonstrations are included.

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. Almond, R.G.: Graphical Belief Modeling. Chapman & Hall, London (1995)

    Google Scholar 

  2. Ayoun, A., Smets, P.: Data association in multi-target detection using the transferable belief model. Int. Journal of Intelligent Systems 16(10), 1167–1182 (2001)

    Article  MATH  Google Scholar 

  3. Cobb, B.R., Shenoy, P.P.: A Comparison of Methods for Transforming Belief Functions Models to Probability Models. In: Nielsen, T.D., Zhang, N.L. (eds.) ECSQARU 2003. LNCS (LNAI), vol. 2711, pp. 255–266. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  4. Daniel, M.: Algebraic structures related to Dempster-Shafer theory. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds.) IPMU 1994. LNCS, vol. 945, pp. 51–61. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  5. Daniel, M.: Distribution of Contradictive Belief Masses in Combination of Belief Functions. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds.) Information, Uncertainty and Fusion, pp. 431–446. Kluwer Academic Publishers, Boston (2000)

    Chapter  Google Scholar 

  6. Daniel, M.: Algebraic Structures Related to the Combination of Belief Functions. Scientiae Mathematicae Japonicae 60(2), 245–255 (2004); Sci. Math. Jap. Online 10, 501–511 (2004)

    Google Scholar 

  7. Daniel, M.: Probabilistic Transformations of Belief Functions. In: Godo, L. (ed.) ECSQARU 2005. LNCS (LNAI), vol. 3571, pp. 539–551. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Daniel, M.: New Approach to Conflicts within and between Belief Functions. Technical report V-1062, ICS AS CR, Prague (2009)

    Google Scholar 

  9. Daniel, M.: Conflicts within and between Belief Functions. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS (LNAI), vol. 6178, pp. 696–705. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  10. Daniel, M.: Conflicts of Belief Functions. Technical report V-1108, ICS AS CR, Prague (2011)

    Google Scholar 

  11. Daniel, M.: Introduction to an Algebra of Belief Functions on Three-element Frame of Discernment — A Quasi Bayesian Case. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) IPMU 2012, Part III. CCIS, vol. 299, pp. 532–542. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  12. Haenni, R.: Aggregating Referee Scores: an Algebraic Approach. In: 2nd International Workshop on Computational Social Choice, COMSOC 2008, Liverpool, UK (2008)

    Google Scholar 

  13. Hájek, P., Havránek, T., Jiroušek, R.: Uncertain Information Processing in Expert Systems. CRC Press, Boca Raton (1992)

    Google Scholar 

  14. Hájek, P., Valdés, J.J.: Generalized algebraic foundations of uncertainty processing in rule-based expert syst. (dempsteroids). Comp. and Artif. Intell. 10, 29–42 (1991)

    MATH  Google Scholar 

  15. Liu, W.: Analysing the degree of conflict among belief functions. Artificial Intelligence 170, 909–924 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  17. Smets, P.: The combination of evidence in the transferable belief model. IEEE-Pattern Analysis and Machine Intelligence 12, 447–458 (1990)

    Article  Google Scholar 

  18. Smets, P.: Analyzing the combination of conflicting belief functions. Information Fusion 8, 387–412 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, CZ – 182 07, Prague 8, Czech Republic

    Milan Daniel

Authors
  1. Milan Daniel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Armii Krajowej 36, 42-200, Częstochowa, Poland

    Leszek Rutkowski , Marcin Korytkowski  & Rafał Scherer ,  & 

  2. AGH University of Science and Technology, Michiewicza 30, 30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  3. Department of Electrical Engineering and Computer Sciences, University of California, 94720-1776, Berkeley, CA, USA

    Lotfi A. Zadeh

  4. Electrical and Computer Engineering, University of Louisville, 405 Lutz Hall, 40292, Louisville, KY, USA

    Jacek M. Zurada

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Daniel, M. (2013). Properties of Plausibility Conflict of Belief Functions. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2013. Lecture Notes in Computer Science(), vol 7894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38658-9_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38658-9_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38657-2

  • Online ISBN: 978-3-642-38658-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation