Attribute Reduction in Random Information Systems with Fuzzy Decisions

  • Wei-Zhi Wu
  • You-Hong Xu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6743)


Knowledge reduction is one of the main problems in the study of rough set theory. This paper deals with knowledge reduction in the sense of reducing attributes in random information systems with fuzzy decisions based on the Dempster-Shafer theory of evidence. The concepts of lower approximation reducts, upper approximation reducts, random belief reducts and random plausibility reducts in random fuzzy decision systems are introduced. The relationships among these reducts are examined.


Belief functions fuzzy decisions knowledge reduction random information systems rough sets 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Lingras, P.J., Yao, Y.Y.: Data mining using extensions of the rough set model. Journal of the American Society for Information Science 49, 415–422 (1998)CrossRefGoogle Scholar
  2. 2.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Boston (1991)CrossRefzbMATHGoogle Scholar
  3. 3.
    Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)zbMATHGoogle Scholar
  4. 4.
    Skowron, A.: The rough sets theory and evidence theory. Fundamenta Informaticae 13, 245–262 (1990)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Wu, W.-Z.: A comparative study of belief and plausibility reducts in information systems with fuzzy decisions. In: Proceedings of 2010 International Conference on Machine Learning and Cybernetics (ICMLC 2010), Qingdao, China, July 11-14, pp. 552–557 (2010)Google Scholar
  6. 6.
    Wu, W.-Z.: Attribute reduction based on evidence theory in incomplete decision systems. Information Sciences 178, 1355–1371 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Wu, W.-Z., Leung, Y., Mi, J.-S.: On generalized fuzzy belief functions in infinite spaces. IEEE Transactions on Fuzzy Systems 17, 385–397 (2009)CrossRefGoogle Scholar
  8. 8.
    Wu, W.-Z., Leung, Y., Zhang, W.-X.: Connections between rough set theory and Dempster-Shafer theory of evidence. International Journal of General Systems 31, 405–430 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Wu, W.-Z., Zhang, M., Li, H.-Z., Mi, J.-S.: Knowledge reduction in random information systems via Dempster-Shafer theory of evidence. Information Sciences 174, 143–164 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Yao, Y.Y.: Interpretations of belief functions in the theory of rough sets. Information Sciences 104, 81–106 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Zadeh, L.A.: Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23, 421–427 (1968)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Zhang, M., Xu, L.D., Zhang, W.-X., Li, H.-Z.: A rough set approach to knowledge reduction based on inclusion degree and evidence reasoning theory. Expert Systems 20, 298–304 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Wei-Zhi Wu
    • 1
  • You-Hong Xu
    • 1
  1. 1.School of Mathematics, Physics and Information ScienceZhejiang Ocean UniversityZhoushanP.R. China

Personalised recommendations