Uncertainty and Feature Selection in Rough Set Theory

  • Jiye Liang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6954)

Abstract

In rough set theory, the uncertainty of granulation and efficient feature selection algorithms have attracted much attention in recent years. We focus on the review of several common uncertainty measures and the relationships among them. An efficient accelerator is developed to accelerate a heuristic process of feature selection.

Keywords

Rough set information entropy information granulation granular space distance feature selection 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bazan, J., Peters, J.F., Skowron, A., Nguyen, H.S., Szczuka, M.: Rough Set Approach to Pattern Extraction from Classifiers. J. Electron. Notes Theoretica. Comput. Sci. 82, 20–29 (2003)CrossRefMATHGoogle Scholar
  2. 2.
    Hu, X.H., Cercone, N.: Learning in relational databases: a rough set approach. Int. J. Comput. Intell. 11, 323–338 (1995)Google Scholar
  3. 3.
    Hu, Q.H., Xie, Z.X., Yu, D.R.: Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation. Pattern Recognit. 40, 3509–3521 (2007)CrossRefMATHGoogle Scholar
  4. 4.
    Grzymala-Busse, J.W.: An algorithm for computing a single covering. In: Grzymala-Busse, J.W. (ed.) Managing Uncertainty in Expert Systems, p. 66. Kluwer Academic Publishers, Netherlands (1991)CrossRefGoogle Scholar
  5. 5.
    Kryszkiewicz, M., Lasek, P.: FUN: fast discovery of minimal sets of attributes functionally determining a decision attribute. Trans. Rough Sets 9, 76–95 (2008)Google Scholar
  6. 6.
    Liang, J.Y., Dang, C.Y., Chin, K.S., Yam Richard, C.M.: A new method for measuring uncertainty and fuzziness in rough set theory. Int. J. General Syst. 31, 331–342 (2002)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Liang, J.Y., Shi, Z.Z.: The information entropy, rough entropy and knowledge granulation in rough set theory. Int. J. Uncertain., Fuzziness Knowl.-Based Syst. 12, 37–46 (2004)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Liang, J.Y., Shi, Z.Z., Li, D.Y., Wierman, M.J.: The information entropy, rough entropy and knowledge granulation in incomplete information system. Int. J. General Syst. 35, 641–654 (2006)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Liang, J.Y., Qian, Y.H.: Information granules and entropy theory in information systems. Sci. China., Ser. F. 51, 1427–1444 (2008)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Nguyen, H.S., Ślęzak, D.: Approximate reducts and association rules correspondence and complexity results. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 137–145. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  11. 11.
    Pedrycz, W., Vukovich, G.: Feature analysis through information granulation and fuzzy sets. Pattern Recognit. 35, 825–834 (2002)CrossRefMATHGoogle Scholar
  12. 12.
    Pawlak, Z.: Rough Sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Boston (1991)CrossRefMATHGoogle Scholar
  13. 13.
    Pawlak, Z., Skowron, A.: Rudiments of rough sets. Inf. Sci. 177, 3–27 (2007)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Qian, Y.H., Liang, J.Y., Pedrycz, W., Dang, C.Y.: Positive approximation: an accelerator for attribute reduction in rough set theory. Artifi. Intell. 174, 597–618 (2010)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Qian, Y.H., Liang, J.Y.: Combination entropy and combination granulation in rough set theory. Int. J. Uncertain., Fuzziness Knowl.-Based Syst. 16, 179–193 (2008)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Qian, Y.H., Liang, J.Y., Dang, C.Y.: Knowledge structure, knowledge granulation and knowledge distance in a knowledge base. Int. J. Approx. Reasoning 50, 174–188 (2009)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Shannon, C.E.: A mathematical theory of communication. The Bell System Technology Journal 21, 372–423, 623–656 (1948)CrossRefMATHGoogle Scholar
  18. 18.
    Skowron, A.: Extracting laws from decision tables: a rough set approach. Comput. Intell. 11, 371–388 (1995)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Slezak, D.: Approximate entropy reducts. Fundam. Inform. 53, 365–390 (2002)MathSciNetMATHGoogle Scholar
  20. 20.
    Wang, G.Y., Yu, H., Yang, D.C.: Decision table reduction based on conditional information entropy. Chin. J. Comput. 25, 759–766 (2002)MathSciNetGoogle Scholar
  21. 21.
    Wierman, M.J.: Measuring uncertainty in rough set theory. Int. J. General Syst. 28, 283–297 (1999)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Yao, J.T., Yao, Y.Y.: Information granulation for Web based information retrieval support systems. In: Data Mining and Knowledge Discovery: Theory, Tools and Technology. SPIE, vol. 5098, pp. 138–146 (2003)Google Scholar
  23. 23.
    Yao, Y.Y., Zhao, Y.: Attribute reduction in decision-theoretic rough set models. Inf. Sci. 178, 3356–3373 (2008)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Yao, Y.Y.: Neighborhood systems and approximate retrieval. Inf. Sci. 176, 3431–3452 (2006)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Ziarko, W.: Variable precision rough set model. J. Comput. Syst. Sci. 46, 39–59 (1993)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jiye Liang
    • 1
  1. 1.Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, School of Computer and Information TechnologyShanxi UniversityTaiyuanChina

Personalised recommendations