Skip to main content
SpringerLink
Log in
Book cover

Portuguese Conference on Artificial Intelligence

EPIA 1997: Progress in Artificial Intelligence pp 155–166Cite as

Measures of uncertainty and independence concept in different calculi

  • Knowledge Representation
  • Conference paper
  • First Online:

  • 99 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1323))

Abstract

This contribution studies the relationship between measures of uncertainty and the independence (or noninteractiveness) concepts in probability theory, Dempster-Shafer theory and possibility theory. Although Shannon entropyis very strong tool when studying independence and conditional independence relations in probability theory, its nonprobabilistic counterparts (i.e. amount of uncertainty in Dempster-Shafer theory and measure of nonspecificity in possibility theory) seem not to play this role, which is demonstrated by simple examples. Moreover, it is argued, why amount of uncertainty — although used in possibility theory — is not appropriate measure of uncertainty within this framework.

The work on this paper was partially supported by Grant no. VS96008 of the Minisry of Education of the Czech Republic.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aczél, J., Daróczy, Z.: On measures of information and their characterizations, Academic Press, New York, San Francisco, London, 1975.

    Google Scholar 

  2. Dubois, D., Prade H.: Possibility theory. Plenum Press, New York, 1988.

    Google Scholar 

  3. Gallager, R.R.: Information Theory and Reliable Communication, New York, Wiley, 1968.

    Google Scholar 

  4. Geer, J. F., Klir, G.J.: Discord in possibility theory. Intern. J. of General Systems, 19 (1991), 119–132.

    Google Scholar 

  5. George, T., Pal, N.R.: Quantification of conflict in Dempster-Shafer framework: a new approach. Intern. J. of General Systems, 24 (1996), 407–423.

    Google Scholar 

  6. Guan, J. W., Bell, J.W.: Evidence Theory and Applications (Vol. 1). North-Holland, Amsterdam and New York, 1991.

    Google Scholar 

  7. Harmanec, D., Klir G.J.: Measuring total uncertainty in Dempster-Shafer theory: a novel approach. Intern. J. of General Systems, 22 (1994), 405–419.

    Google Scholar 

  8. Harmanec, D., Resconi, G., Klir, G.J. and Pan, Y.: On the computation of the uncertainty measure for the Dempster-Shafer theory. Intern. J. of General Systems, 25 (1996), 153–163.

    Google Scholar 

  9. Hartley, R.V.L.: Transmission of information. The Bell Systems Technical J., 7 (1928), 535–563.

    Google Scholar 

  10. Höhle, V.: Entropy with respect to plausibility measures. Proc. 12th IEEE Symp. on Multiple-Valued Logic, Paris, 167–169.

    Google Scholar 

  11. Jaffray, J.Y.: On the maximum-entropy probability which is consistent with convex capacity. Intern. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, 3 (1995), 27–33.

    Google Scholar 

  12. Klir, G.J., Folger, T.A.: Fuzzy Sets, Uncertainty, and Information. Prentice Hall, Englewood Cliffs, NJ, 1988.

    Google Scholar 

  13. Klir, G.J., Mariano, M.: On the uniqueness of possibilistic measure of uncertainty and information. Fuzzy sets and systems, 24 (1987), 197–219.

    Google Scholar 

  14. Klir, G.J., Parviz, P. A note on the measure of discord. Proc. Eighth Conf. on Uncertainty in AI (D. Dubois et al., editors), San Mateo, California, Morgan Kaufman, 1992, 138–141.

    Google Scholar 

  15. Klir, G.J., Ramer, A.: Uncertainty in the Dempster-Shafer theory: A critical reexamination. Intern. J. General Systems 18 (1990), 155–166.

    Google Scholar 

  16. Lamata, M.T., Moral, S.: Measures of entropy in the theory of evidence. Intern. J. of General Systems, 14 (1988), 297–305.

    Google Scholar 

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

    Google Scholar 

  18. Ramer, A., Diamond P., Padet, C.: Total Uncertainty Revisited. Intern. J. of General Systems (submitted).

    Google Scholar 

  19. Ramer, A.: Uniqueness of information measure in the theory of evidence. Fuzzy Sets and Systems 24 (1987), 193–196.

    Google Scholar 

  20. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton, 1976.

    Google Scholar 

  21. Shannon, C.E.: The mathematical theory of communication. The Bell System Technical J., 27 (1948), 379–423, 623–665.

    Google Scholar 

  22. Shenoy, P.P.: Conditional independence in valuation-based systems. Intern. J. of Approximate Reasoning, 10 (1994), 203–234.

    Google Scholar 

  23. Studený, M.: Multiinformation and the problem of characterization of conditional independence relations. Problems of Control and Information Theory, 18 (1989), 3–16.

    Google Scholar 

  24. Studený, M.: Formal properties of conditional independence in different calculi of Al. Symbolic and Quantitative Approaches to Reasoning and Uncertainty (M. Clarke, R. Kruse and S. Moral eds.), Lecture Notes in Computer Science 747, Springer-Verlag, 341–348.

    Google Scholar 

  25. Vejnarová, J.: A few remarks on measures of uncertainty in Dempster-Shafer theory. Intern. J. of General Systems, 22 (1994), 233–243.

    Google Scholar 

  26. Vejnarová, J., Klir, G.J.: Measure of strife in Dempster-Shafer theory. Intern. J. of General Systems, 22 (1993), 25–42.

    Google Scholar 

  27. Yager, R.: Entropy and specificity in a mathematical theory of evidence. Intern. J. of General Systems, 9 (1983), 249–260.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Intelligent Systems, University of Economics Ekonomická 957, CZ-148 00, Prague

    Jiřina Vejnarová

  2. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodárenskou, CZ-182 08, Prague, Czech Republic

    Jiřina Vejnarová

Authors
  1. Jiřina Vejnarová
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ernesto Coasta Amilcar Cardoso

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Vejnarová, J. (1997). Measures of uncertainty and independence concept in different calculi. In: Coasta, E., Cardoso, A. (eds) Progress in Artificial Intelligence. EPIA 1997. Lecture Notes in Computer Science, vol 1323. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023919

Download citation

  • DOI: https://doi.org/10.1007/BFb0023919

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63586-4

  • Online ISBN: 978-3-540-69605-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation