Skip to main content

A global measure of ambiguity for classification

  • Communications
  • Conference paper
  • First Online:
Methodologies for Intelligent Systems (ISMIS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 869))

Included in the following conference series:

  • 147 Accesses

Abstract

This paper suggests a a global measure of ambiguity based on the notion of an interval structure which can be viewed as a qualitative measure of belief. It is shown that the boundary region in the roughset model is a special case of the proposed measure. To demonstrate the usefulness of this new measure, it is being used as a criterion for selecting appropriate attributes in the construction of decision trees.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bundy, A., (1985), “Incidence Calculus: a Mechanism for Probabilistic Reasoning”, Journal of Automated Reasoning, 1, 263–283.

    Google Scholar 

  • Dubois, D. and Prade, H., (1988), “Rough Fuzzy Sets and Fuzzy Rough Sets”, Internal Conference on Fuzzy Sets in Informatics, Moscow, September, 20–30.

    Google Scholar 

  • Feller, W., (1968), An Introduction to Probability Theory and Its Applications. John Wiley & Sons.

    Google Scholar 

  • Fine, T., (1973), Theories of Probability. Academic Press, New York

    Google Scholar 

  • Fishburn, P.C., (1991), “On the Theory of Ambiguity”, Information and Management Sciences, 2, 1–16.

    Google Scholar 

  • Fishburn, P.C., (1992), “The Axioms and Algebra of Ambiguity”, private communication.

    Google Scholar 

  • Kruse, R., Schwecke, E., and Heinsohn, J., (1991), Uncertainty and Vagueness in Knowledge Based Systems. Springer-Verlag, Berlin.

    Google Scholar 

  • Pawlak, Z., (1982), “Rough Sets”, Internal Journal of Information and Computer Sciences, 11, 341–356.

    Google Scholar 

  • Pawlak, Z., (1991), Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht, The Netherlands.

    Google Scholar 

  • Pearl, J., (1988), Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers.

    Google Scholar 

  • Prerau, D.S., (1990), Developing and Managing Expert Systems: Proven Techniques for Business and Industry. Addison-Wesley Publishing Company, Inc.

    Google Scholar 

  • Savage, L.J., (1972), The Foundations of Statistics, Dover, New York.

    Google Scholar 

  • Slowinski R. (ed.), (1992), Intelligent Decision Support Handbook of Applications and Advances of the Rough Sets Theory. Kluwer Academic Publishers, Dordrecht, The Netherlands.

    Google Scholar 

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

    Google Scholar 

  • Shafer, G., (1987), “Belief Functions and Possibility Measures”, Analysis of Fuzzy Information, Vol. 1: Mathematics and Logic, Bezdek, J.C. Ed. Boca Raton, FL: CRC Press, 51–84.

    Google Scholar 

  • Smets, P., (1988), “Belief Functions (with Discussion)” in Non-Standard Logics for Automated Reasoning. Smets, P., Mamdani, A., Dubois, D., and Prade, H., Eds. New York: Academic, 282–285.

    Google Scholar 

  • Smets, P., (1990), “The Combination of Evidence in the Transferable Belief Model,” IEEE Trans. Pattern Anal. Machine Intell., 12, 447–458.

    Google Scholar 

  • Wong, S.K.M., Wang, L.S., and Yao, Y.Y., (1992), “Interval Structure: a Framework for Representing Uncertain Information”, Proceedings of the 8th Conference on Uncertainty in Artificial Intelligence, 336–343.

    Google Scholar 

  • Wong, S.K.M. and Wang, Z.W., (1993), “Qualitative Measures of Ambiguity”, Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence, 443–450

    Google Scholar 

  • Zadeh, L.A., (1965), “Fuzzy Sets”, Information and Control, 8, 338–353.

    Google Scholar 

  • Ziarko, W., (1992), “Variable Precision Rough Set Model”, J. of Computer and System Sciences, 46(1).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Zbigniew W. Raś Maria Zemankova

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, Z.W., Wong, S.K.M. (1994). A global measure of ambiguity for classification. In: Raś, Z.W., Zemankova, M. (eds) Methodologies for Intelligent Systems. ISMIS 1994. Lecture Notes in Computer Science, vol 869. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58495-1_11

Download citation

  • DOI: https://doi.org/10.1007/3-540-58495-1_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58495-7

  • Online ISBN: 978-3-540-49010-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics