Skip to main content
SpringerLink
Log in

Classic Works of the Dempster-Shafer Theory of Belief Functions: An Introduction

  • Chapter
Book cover Classic Works of the Dempster-Shafer Theory of Belief Functions

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 219))

Abstract

In this chapter, we review the basic concepts of the theory of belief functions and sketch a brief history of its conceptual development. We then provide an overview of the classic works and examine how they established a body of knowledge on belief functions, transformed the theory into a computational tool for evidential reasoning in artificial intelligence, opened up new avenues for applications, and became authoritative resources for anyone who is interested in gaining further insight into and understanding of belief functions.

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 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover 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. Bernoulli, J. The Art of Conjecturing: Together with His Letter to a Friend on Sets in Court Tennis. Johns Hopkins University Press, 2006. Translated by Edith Dudley Sylla.

    Google Scholar 

  2. Boole, G. An Investigation into the Laws of Thought. Walton and Maberly, London, 1854. Reprinted 1951, Dover, NY.

    Google Scholar 

  3. Carnap, R. Meaning and Necessity. University of Chicago Press, Chicago, Illinois, 1956.

    Google Scholar 

  4. Choquet, G. Theory of capacities. Ann. Inst. Fourier 5 (1953), 131–295.

    Google Scholar 

  5. Dempster, A. P On direct probabilities. Journal of the Royal Statistical Society Series B 25 (1962), 100–110.

    MathSciNet  Google Scholar 

  6. Dempster, A. P Further examples of inconsistencies in the fiducial argument. Annals of Mathematical Statistics 34 (1963), 884–891.

    Article  MathSciNet  MATH  Google Scholar 

  7. Dempster, A. P On the difficulties inherent in Fisher’s fiducial argument. J. Amer. Statist. Assoc. 59 (1964), 56–66.

    Article  MATH  MathSciNet  Google Scholar 

  8. Dempster, A. P New methods for reasoning towards posterior distributions based on sample data. Annals of Mathematical Statistics 37 (1966), 355–374.

    Article  MathSciNet  MATH  Google Scholar 

  9. Dempster, A. P Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 38 (1967), 325–339.

    Article  MathSciNet  MATH  Google Scholar 

  10. Dempster, A. P A generalization of Bayesian inference (with discussion). Journal of the Royal Statistical Society Series B 30 (1968), 205–247.

    MathSciNet  Google Scholar 

  11. Dempster, A. P Belief functions in the 21st century: A statistical perspective. In Proceedings of Insitute for Operations Research and Management Science Annual Meeting (INFORMS-2001) (Miami Beach, FL, 2001).

    Google Scholar 

  12. Dempster, A. P The Dempster-Shafer calculus for statisticians. International Journal of Approximate Reasoning (2006), in press.

    Google Scholar 

  13. Drucker, H., Schapire, R. E., and Simard, P. Y. Boosting performance in neural networks. International Journal of Pattern Recognition and Artificial Intelligence 7 (1993), 705–719.

    Article  Google Scholar 

  14. Einstein, A., and Infeld, L. The Evolution of Physics. Simon and Schuster, New York, 1961.

    Google Scholar 

  15. Fagin, R., and Halpern, J. Y. A new approach to updating beliefs. In Uncertainty in Artificial Intelligence 6, P. P. Bonissone, M. Henrion, L. N. Kanal, and J. F. Lemmer, Eds. Morgan Kaufmann, San Mateo, CA, 1991, pp. 317–325.

    Google Scholar 

  16. Fishburn, P. Decision and Value Theory. Wiley, New York, 1964.

    MATH  Google Scholar 

  17. Fisher, R. A Inverse probability. Proc. Camb. Phil. Soc. 26 (1930), 154–57, 172–173. Reprinted in Bennett, J. H. (1971). Collected Papers of R. A. Fisher 2, Univ. of Adelaide.

    Article  Google Scholar 

  18. Good, I. The measure of a non-measurable set. In Logic, Methodology and Philosophy of Science, E. Nagel, P. Suppes, and A. Tarski, Eds. Stanford University Press, Stanford, 1962, pp. 319–329.

    Google Scholar 

  19. Hacking, I. The Emergence of Probability. Cambridge University Press, New York, 1975.

    MATH  Google Scholar 

  20. Kearns, M., and Valiant, L. Cryptographic limitations on learning Boolean formulae and finite automata. Journal of the ACM 41 (1994), 67–95.

    Google Scholar 

  21. Kohlas, J., and Monney, P.-A. A Mathematical Theory of Hints. Springer, 1995.

    Google Scholar 

  22. Kong, A. Multivariate Belief Functions and Graphical Models. PhD thesis, Department of Statistics, Harvard University, Cambridge, MA, 1986.

    Google Scholar 

  23. Laskey, K. B., and Lehner, P. E. Assumption, belief and probabilities. Artificial Intelligence 41 (1989), 65–77.

    Article  MathSciNet  Google Scholar 

  24. Lauritzen, S. L., and Spiegelhalter, D. J. Local computations with probabilities on graphical structures and their application to expert systems (with discussion). Journal of the Royal Statistical Society Series B 50 (1988), 157–224.

    MATH  MathSciNet  Google Scholar 

  25. Liu, L. A note on Luce-Fishburn axiomatization of rank-dependent utility. Journal of Risk and Uncertainty 28, 1 (2004), 55–71.

    Article  MATH  Google Scholar 

  26. Luce, R. D., and Fishburn, P. C. A note on deriving rank-dependent linear utility using additive joint receipts. Journal of Risk and Uncertainty 11 (1995), 5–16.

    Article  MATH  Google Scholar 

  27. Pal, N. R., Bezdek, J. C., and Hemasinha, R. Uncertainty measures for evidential reasoning II: A new measure of total uncertainty. International Journal of Approximate Reasoning 8 (1993), 1–16.

    Google Scholar 

  28. Pearl, J. Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Mateo, CA, 1988.

    Google Scholar 

  29. Pearl, J. Reasoning with belief functions: An analysis of compatibility. International Journal of Approximate Reasoning 4 (1990), 363–389.

    Google Scholar 

  30. Quiggin, J. A theory of anticipated utility. Journal of Economic Behavior and Organization 3 (1982), 323–343.

    Article  Google Scholar 

  31. Ruspini, E. H The logical foundations of evidential reasoning. Tech. rep., SRI International, Menlo Park, California, 1986.

    Google Scholar 

  32. Savage, L. J The Foundations of Statistics. Wiley, New York, NY, 1954.

    MATH  Google Scholar 

  33. Schapire, R. E The strength of weak learnability. Machine Learning 5 (1990), 197–227.

    Google Scholar 

  34. Shafer, G. A Mathematical Theory of Evidence. Princeton University Press, Princeton, NJ, 1976.

    MATH  Google Scholar 

  35. Shafer, G. Belief functions and possibility measures. In The Analysis of Fuzzy Information, J. Bezdek, Ed., vol. 1. CRC Press, Boca Raton, FL, 1987, pp. 51–84.

    Google Scholar 

  36. Smets, P. Un mod童 math謡tico-statistique simulant le processus du diagnostic m裩cal. PhD thesis, Universit矌ibre de Bruxelles, Bruxelles, Belgium, 1978.

    Google Scholar 

  37. Smets, P. Probability of provability and belief functions. Logique et Analyse 133-134 (1993), 177–195.

    MathSciNet  Google Scholar 

  38. Smith, C. A. B. Consistency in statistical inference and decision (with discussion). Journal of the Royal Statistical Society Series B 23 (1961), 1–25.

    Google Scholar 

  39. Smith, C. A. B. Personal probability and statistical analysis (with discussion). Journal of the Royal Statistical Society Series A 128 (1965), 469–499.

    Google Scholar 

  40. Srivastava, R. R., and Shafer, G. Belief-function formulas for audit risk. The Accounting Review 67, 2 (1992), 249–283.

    Google Scholar 

  41. Sung, B. Translations from James Bernoulli (with a preface by A. P. Dempster). Department of Statistics, Harvard University, Cambridge, Massachusetts, 1966.

    Google Scholar 

  42. Zadeh, L. A Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1 (1978), 3–28.

    Article  MATH  MathSciNet  Google Scholar 

  43. Zadeh, L. A Review of A Mathematical Theory of Evidence. AI Magazine 5 (1984), 81.

    Google Scholar 

Download references

Authors
  1. Liping Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ronald R. Yager
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Machine Intelligence Institute, Iona College, 715 N. Avenue, New Rochelle, NY 10801-1890, USA

    Roland R. Yager (Dr.) (Dr.)

  2. Department of Management and Information Systems, University of Akron College of Business Administration, 351 Akron, OH 4325-4801, USA

    Liping Liu

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Liu, L., Yager, R.R. (2008). Classic Works of the Dempster-Shafer Theory of Belief Functions: An Introduction. In: Yager, R.R., Liu, L. (eds) Classic Works of the Dempster-Shafer Theory of Belief Functions. Studies in Fuzziness and Soft Computing, vol 219. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44792-4_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-44792-4_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25381-5

  • Online ISBN: 978-3-540-44792-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation