An Introduction to the Theory of Plausible and Paradoxical Reasoning | SpringerLink
Skip to main content

An Introduction to the Theory of Plausible and Paradoxical Reasoning

  • Conference paper
  • First Online:
Numerical Methods and Applications (NMA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2542))

Included in the following conference series:

  • 1197 Accesses

Abstract

This paper presents the basic mathematical settings of a new theory of plausible and paradoxical reasoning and describes a rule of combination of sources of information in a very general framework where information can be both uncertain and paradoxical. Within this framework, the rule of combination which takes into account explicitly both conjunctions and disjunctions of assertions in the fusion process, appears to be more simple and general than the Dempster’s rule of combination. Through two simple examples, we show the strong ability of this new theory to solve practical but difficult problems where the Dempster-Shafer theory usually fails.

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 11439
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 14299
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. Cheng Y., Kashyap R.L., “Study of the Different Methods for Combining Evidence”, Proceedings of SPIE on Applications of Artificial Intelligence, Vol. 635, pp. 384–393, 1986.

    Google Scholar 

  2. Dedekind R.,” Über Zerlegungen von Zhalen durch ihre grössten gemeinsammen Teiler”, In Gesammelte Werke, Bd. 1., pp. 103–148, 1897.

    Google Scholar 

  3. Dezert J., “Autonomous Navigation with Uncertain Reference Points using the PDAF”, Chapter 9 in Multitarget-Multisensor Tracking: Applications and Advances, Vol. 2, pp. 271–324, Y. Bar-Shalom Editor, Artech House, 1991.

    Google Scholar 

  4. Dezert J., “Optimal Bayesian Fusion of Multiple Unreliable Classifiers”, Proceedings of 4th Intern. Conf. on Information Fusion (Fusion 2001), Montréal, Aug. 7–10, 2001.

    Google Scholar 

  5. Dezert J., “Foundations for a new theory of plausible and paradoxical reasoning”, To appear in next issue of the International Journal of Information & Security, edited by Prof. Tzv. Semerdjiev, CLPP, Bulgarian Academy of Sciences, 40 pages, 2002.

    Google Scholar 

  6. Dubois D., Prade H.,“Théories des Possibilités. Application à la Représentation des Connaissances en Informatique”, Editions Masson, Paris, 1985.

    Google Scholar 

  7. Dubois D., Garbolino P., Kyburg H.E., Prade H., Smets, Ph., “Quantified Uncertainty”, J. Applied Non-Classical Logics, Vol.1, pp. 105–197, 1991.

    MATH  MathSciNet  Google Scholar 

  8. Klawonn F., Smets Ph., “The dynamic of belief in the transferable belief model and specialization-generalization matrices”, in Uncertainty in Artificial Intelligence 92, pp 130–137, Dubois D. and Wellman M. P. and D'Ambrosio B. and Smet, Ph. Editors, Morgan Kaufman, San Mateo, Ca, 1992.

    Google Scholar 

  9. Mahler R., “Combining Ambiguous Evidence with Respect to Abiguous a priori Knowledge, I: Boolean Logic”, IEEE Trans. on SMC, Part 1: Systems and Humans, Vol. 26, No. 1, pp. 27–41, 1996.

    Article  Google Scholar 

  10. Shafer G., “A Mathematical Theory of Evidence”, Princeton University Press, Princeton, New Jersey, 1976.

    MATH  Google Scholar 

  11. Shafer G., Tversky A., “Languages and designs for probability”, Cognitive Sc., Vol.9, pp. 309–339, 1985.

    Article  Google Scholar 

  12. Smarandache F., “An Unifying Field in Logics: Neutrosophic Logic”, (Second Edition), American Research Press, Rehoboth, 2000 (ISBN 1-879585-76-6).

    Google Scholar 

  13. Smets Ph.,“The Combination of Evidence in the Transferable Belief Model”, IEEE Trans. on PAMI, Vol. 12, no. 5, 1990.

    Google Scholar 

  14. Smets Ph.,“The alpha-junctions: combination operators applicable to belief function”, Qualitative and quantitative practical reasoning, Springer, Gabbay D.M and Kruse R. and Nonnengart A. and Ohlbach H.J. Editors, pp. 131–153, 1997.

    Google Scholar 

  15. Smets Ph.,“The transferable belief model for quantified belief representation”, Handbook of Defeasible Reasoning and Uncertainty Management Systems, D. M. Gabbay and Ph. Smets (Editors), Vol. 1, Kluwer, Doordrecht, The Netherlands, 1998.

    Google Scholar 

  16. Smets Ph., “Data Fusion in the Transferable Belief Model”, Proceedings of 3rd Int. Conf. on Inf. Fusion (Fusion 2000), pp. PS–21–PS33, Paris, July 10–13, 2000 (http://www.onera.fr/fusion2000)

  17. Sun H., he K., Zhang B.,“The Performance of Fusion Judgment on Dempster-Shafer Rule”, Chinese Journal of Electronics, Vol. 8, no. 1, Jan. 1999.

    Google Scholar 

  18. Zadeh L.A.,“A Theory of Approximate Reasoning” Machine Intelligence, J. Hayes, D. Michie and L. Mikulich Eds, Vol. 9, pp. 149–194, 1979.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dezert, J. (2003). An Introduction to the Theory of Plausible and Paradoxical Reasoning. In: Dimov, I., Lirkov, I., Margenov, S., Zlatev, Z. (eds) Numerical Methods and Applications. NMA 2002. Lecture Notes in Computer Science, vol 2542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36487-0_2

Download citation

  • DOI: https://doi.org/10.1007/3-540-36487-0_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00608-4

  • Online ISBN: 978-3-540-36487-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics