Advertisement

An Information-Theoretic Interpretation of Thresholds in Probabilistic Rough Sets

  • Xiaofei Deng
  • Yiyu Yao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7414)

Abstract

In a probabilistic rough set model, the positive, negative and boundary regions are associated with classification errors or uncertainty. The uncertainty is controlled by a pair of thresholds defining the three regions. The problem of searching for optimal thresholds can be formulated as the minimization of uncertainty induced by the three regions. By using Shannon entropy as a measure of uncertainty, we present an information-theoretic approach to the interpretation and determination of thresholds.

Keywords

Equivalence Class Boundary Region Shannon Entropy Conditional Entropy Entropy Minimization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Azam, N., Yao, J.: Multiple Criteria Decision Analysis with Game-theoretic Rough Sets. In: Li, T., Nguyen, H.S., Wang, G., Grzymala-Busse, J.W., Janicki, R., Hassanien, A.E., Yu, H. (eds.) RSKT 2012. LNCS (LNAI), vol. 7414, pp. 400–409. Springer, Heidelberg (2012)Google Scholar
  2. 2.
    Herbert, J.P., Yao, J.T.: Learning optimal parameters in decision-theoretic rough sets. In: Wen, P., Li, Y., Polkowski, L., Yao, Y., Tsumoto, S., Wang, G. (eds.) RSKT 2009. LNCS, vol. 5589, pp. 610–617. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Herbert, J.P., Yao, J.T.: Game-theoretic rough sets. Fundamenta Informaticae 108, 267–286 (2011)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Jia, X., Li, W., Shang, L., Chen, J.: An Optimization Viewpoint of Decision-Theoretic Rough Set Model. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 457–465. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Li, H.X., Zhou, X.Z.: Risk decision making based on decision-theoretic rough set: A three-way view decision model. International Journal of Computational Intelligence Systems 4, 1–11 (2011)CrossRefGoogle Scholar
  6. 6.
    Li, H.X., Zhou, X.Z., Li, T.R., Wang, G.Y., Miao, D.Q., Yao, Y.Y. (eds.): Decision-Theoretic Rough Sets Theory and Recent Research. Science Press, Beijing (2011) (in Chinese)Google Scholar
  7. 7.
    Liu, D., Li, T.R., Ruan, D.: Probabilistic model criteria with decision-theoretic rough sets. Information Science 181, 3709–3722 (2011)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Liu, D., Li, T.R., Li, H.X.: A multiple-category classification approach with decision-theoretic rough sets. Fundamenta Informaticae 115, 173–188 (2012)Google Scholar
  9. 9.
    Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Quinlan, J.R.: Introduction of decision trees. Machine Learning 1, 81–106 (1986)Google Scholar
  11. 11.
    Yao, Y.Y.: Probabilistic approaches to rough sets. Expert Systems 20, 287–297 (2003)CrossRefGoogle Scholar
  12. 12.
    Yao, Y.Y.: Probabilistic rough set approximations. International Journal of Approximate Reasoning 49, 255–271 (2008)zbMATHCrossRefGoogle Scholar
  13. 13.
    Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Information Sciences 180, 341–353 (2010)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Yao, Y.Y.: The superiority of three-way decisions in probabilistic rough set models. Information Science 181, 1080–1096 (2011)zbMATHCrossRefGoogle Scholar
  15. 15.
    Yao, Y.Y.: An Outline of a Theory of Three-Way Decisions. In: Yao, J., Yang, Y., Slowinski, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS (LNAI), vol. 7413, pp. 1–17. Springer, Heidelberg (2012)Google Scholar
  16. 16.
    Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. International Journal of Man-machine Studies 37, 793–809 (1992)CrossRefGoogle Scholar
  17. 17.
    Yao, Y.Y., Wong, S.K.M., Lingras, P.J.: A decision-theoretic rough set model. In: Ras, Z.W., Zemankova, M., Emrich, M.L. (eds.) Methodologies for Intelligent Systems 5, pp. 17–24. North-Holland, New York (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Xiaofei Deng
    • 1
  • Yiyu Yao
    • 1
  1. 1.Department of Computer ScienceUniversity of ReginaReginaCanada

Personalised recommendations