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A global measure of ambiguity for classification

  • Z. W. Wang
  • S. K. M. Wong
Communications Approximate Reasoning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 869)

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.

Keywords

approximate reasoning rough-sets interval structure incidence calculus ambiguity decision trees classification 

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References

  1. Bundy, A., (1985), “Incidence Calculus: a Mechanism for Probabilistic Reasoning”, Journal of Automated Reasoning, 1, 263–283.Google Scholar
  2. 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
  3. Feller, W., (1968), An Introduction to Probability Theory and Its Applications. John Wiley & Sons.Google Scholar
  4. Fine, T., (1973), Theories of Probability. Academic Press, New YorkGoogle Scholar
  5. Fishburn, P.C., (1991), “On the Theory of Ambiguity”, Information and Management Sciences, 2, 1–16.Google Scholar
  6. Fishburn, P.C., (1992), “The Axioms and Algebra of Ambiguity”, private communication.Google Scholar
  7. Kruse, R., Schwecke, E., and Heinsohn, J., (1991), Uncertainty and Vagueness in Knowledge Based Systems. Springer-Verlag, Berlin.Google Scholar
  8. Pawlak, Z., (1982), “Rough Sets”, Internal Journal of Information and Computer Sciences, 11, 341–356.Google Scholar
  9. Pawlak, Z., (1991), Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht, The Netherlands.Google Scholar
  10. Pearl, J., (1988), Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers.Google Scholar
  11. Prerau, D.S., (1990), Developing and Managing Expert Systems: Proven Techniques for Business and Industry. Addison-Wesley Publishing Company, Inc.Google Scholar
  12. Savage, L.J., (1972), The Foundations of Statistics, Dover, New York.Google Scholar
  13. 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
  14. Shafer, G., (1976), A Mathematical Theory of Evidence. Princeton University Press, Princeton.Google Scholar
  15. 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
  16. 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
  17. Smets, P., (1990), “The Combination of Evidence in the Transferable Belief Model,” IEEE Trans. Pattern Anal. Machine Intell., 12, 447–458.Google Scholar
  18. 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
  19. Wong, S.K.M. and Wang, Z.W., (1993), “Qualitative Measures of Ambiguity”, Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence, 443–450Google Scholar
  20. Zadeh, L.A., (1965), “Fuzzy Sets”, Information and Control, 8, 338–353.Google Scholar
  21. Ziarko, W., (1992), “Variable Precision Rough Set Model”, J. of Computer and System Sciences, 46(1).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Z. W. Wang
    • 1
  • S. K. M. Wong
    • 1
  1. 1.Department of Computer ScienceUniversity of ReginaReginaCanada

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