An Optimal Unified Combination Rule | SpringerLink
Skip to main content
Springer Nature Link
Log in

An Optimal Unified Combination Rule

  • Conference paper
Belief Functions: Theory and Applications (BELIEF 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8764))

Included in the following conference series:

Abstract

This paper presents an optimal unified combination rule within the framework of the Dempster-Shafer theory of evidence to combine multiple bodies of evidence. It is optimal in the sense that the resulting combined m-function has the least dissimilarity with the individual m-functions and therefore represents the greatest amount of information similar to that represented by the original m-functions. Examples are provided to illustrate the proposed combination rule.

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

Access this chapter

Log in via an institution

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Chen, W., Cui, Y., He, Y., Yu, Y., Galvin, J., Hussaini, M.Y., Xiao, Y.: Application of Dempster-Shafer theory in dose response outcome analysis. Phys. Med. Biol. 57(2), 5575–5585 (2012)

    Article  Google Scholar 

  2. Cuzzolin, F.: Two new bayesian approximations of belief functions based on convex geometry. IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics 37(4), 993–1008 (2007)

    Article  Google Scholar 

  3. Daniel, M.: Distribution of contradictive belief masses in combination of belief functions. In: Bouchon-Meunier, B., Yager, R., Zadeh, L. (eds.) Information, Uncertainty and Fusion, pp. 431–446. Kluwer Academic Publishers, Boston (2000)

    Chapter  Google Scholar 

  4. Daniel, M.: Comparison between dsm and minc combination rules. In: Smarandache, F., Dezert, J. (eds.) Advances and Applications of DSmT for Information Fusion, pp. 223–240. American Research Press, Rehoboth (2004)

    Google Scholar 

  5. Dempster, A.: New methods for reasoning towards posterior distributions based on sample data. Ann. Math. Statist. 37, 355–374 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dempster, A.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Statist. 38, 325–339 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  7. Denoeux, T.: Inner and outer approximation of belief structures using a hierarchical clustering approach. Int. J. Uncertain. Fuzz. 9(4), 437–460 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dubois, D., Prade, H.: A set-theoretic view of belief functions: logical operations and approximations by fuzzy sets. Int. J. Gen. Syst. 12, 193–226 (1986)

    Article  MathSciNet  Google Scholar 

  9. Florea, M., Jousselme, A., Bossé, É., Grenier, D.: Robust combination rules for evidence theory. Information Fusion 10(2), 183–197 (2009)

    Article  Google Scholar 

  10. Halpern, J., Fagin, R.: Two views of belief: Belief as generalized probability and belief as evidence. Artificial Intelligence 54, 275–318 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  11. He, Y.: Uncertainty Quantification and Data Fusion Baesd on Dempster-Shafer Theory. Ph.D. thesis, Florida State University, Florida, US (December 2013)

    Google Scholar 

  12. Inagaki, T.: Interdependence between safety-control policy and multiple-sensor schemes via Dempster-Shafer theory. IEEE Trans. Rel. 40(2), 182–188 (1991)

    Article  MATH  Google Scholar 

  13. Jousselme, A., Grenier, D., Bossé, É.: A new distance between two bodies of evidence. Information Fusion 2(2), 91–101 (2001)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  15. Kohlas, J., Monney, P.: A Mathematical Theory of Hints: An Approach to Dempster-Shafer Theory of Evidence. Springer, Berlin (1995)

    Book  MATH  Google Scholar 

  16. Lefevre, E., Colot, O., Vannoorenberghe, P.: Belief function combination and conflict management. Information Fusion 3(2), 149–162 (2002)

    Article  Google Scholar 

  17. Sentz, K., Ferson, S.: Combination of evidence in Dempster-Shafer theory. Tech. Rep. SAND 2002-0835, Sandia National Laboratory (2002)

    Google Scholar 

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

    Google Scholar 

  19. Smarandache, F., Dezert, J.: Proportional conflict redistribution rules for information fusion. In: Smarandache, F., Dezert, J. (eds.) Advances and Applications of DSmT for Information Fusion, pp. 3–66. American Research Press, Rehoboth (2006)

    Google Scholar 

  20. Smets, P.: Data fusion in the transferable belief model. In: Proceeding of the Third International Conference on Information Fusion, Paris, France, PS21–PS33 (July 2000)

    Google Scholar 

  21. Smets, P.: Analyzing the combination of conflicting belief functions. Information Fusion 8(4), 387–412 (2007)

    Article  MathSciNet  Google Scholar 

  22. Tessem, B.: Approximations for efficient computation in the theory of evidence. Artificial Intelligence 61(2), 315–329 (1993)

    Article  MathSciNet  Google Scholar 

  23. Yager, R.: On the Dempster-Shafer framework and new combination rules. Information Sciences 41(2), 93–137 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  24. Yager, R.: Quasi-associative operations in the combination of evidence. Kybernetes 16, 37–41 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  25. Zhang, L.: Representation, independence, and combination of evidence in the Dempster-Shafer theory. In: Yager, R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster-Shafer Theory of Evidence, pp. 51–69. John Wiley & Sons, Inc., New York (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Scientific Computing and Imaging Institute, Salt Lake City, Utah, USA

    Yanyan He

  2. Department of Mathematics, Florida State University, Tallahassee, FL, USA

    M. Yousuff Hussaini

Authors
  1. Yanyan He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Yousuff Hussaini
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computing and Communications Technologies, Oxford Brookes University, Wheatley Campus, OX33 1HX, Oxford, UK

    Fabio Cuzzolin

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

He, Y., Hussaini, M.Y. (2014). An Optimal Unified Combination Rule. In: Cuzzolin, F. (eds) Belief Functions: Theory and Applications. BELIEF 2014. Lecture Notes in Computer Science(), vol 8764. Springer, Cham. https://doi.org/10.1007/978-3-319-11191-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-11191-9_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11190-2

  • Online ISBN: 978-3-319-11191-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation