Knowledge Reduction in Inconsistent Decision Tables

  • Qihe Liu
  • Leiting Chen
  • Jianzhong Zhang
  • Fan Min
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4093)


In this paper, we introduce a new type of reducts called the λ-Fuzzy-Reduct, where the fuzzy similarity relation is constructed by means of cosine-distances of decision vectors and the parameter λ is used to tune the similarity precision level. The λ-Fuzzy-Reduct can eliminate harsh requirements of the distribution reduct, and it is more flexible than the maximum distribution reduct, the traditional reduct, and the generalized decision reduct. Furthermore, we prove that the distribution reduct, the maximum distribution reduct, and the generalized decision reduct can be converted into the traditional reduct. Thus in practice the implementations of knowledge reductions for the three types of reducts can be unified into efficient heuristic algorithms for the traditional reduct. We illustrate concepts and methods proposed in this paper by an example.


Decision Table Decision Vector Decision Class Maximum Distribution Fuzzy Equivalence Relation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Pawlak, Z.: Some issues on Rough Sets. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 1–58. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Zhang, W., Mi, J., Wu, W.: Approaches to knowledge reductions in inconsistent information systems. International journal of intelligent systems 18, 989–1000 (2003)CrossRefMATHGoogle Scholar
  3. 3.
    Wen-Xiu, Z., Ju-Sheng, M., Wei-Zhi, W.: Konwledge Reductions in Inconsistent Information Systems. Chinese Journal of Computer 26(1), 12–18 (2003)Google Scholar
  4. 4.
    Ziarko, W.: Variable precision rough set model. Journal of Computer Systems and Science 46, 39–59 (1993)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Nguyen, H.S., Slezak, D.: Approximation 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
  6. 6.
    Slezak, D.: Searching for dynamic reducts in inconsistent decision tables. In: Proceedings of IPMU 1998, Paris, pp. 1362–1369 (1998)Google Scholar
  7. 7.
    Kryszkiewicz, M.: Comparative study of alternative type of knowledge reduction in inconsistent systems. International journal of intelligent systems 16, 105–120 (2001)CrossRefMATHGoogle Scholar
  8. 8.
    Nanda, S.: Fuzzy rough sets. Fuzzy Sets and Systems 45, 157–160 (1992)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Banerjee, M., Pal, S.K.: Roughness of a fuzzy set. Information Science 93, 235–246 (1996)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Lam, W., Ruiz, M., Srinivasan, P.: Automatic taxt categegorization and its application to text retrieval. IEEE Transaction on Knowldge and Data Engineering 11(6), 865–879 (1999)CrossRefGoogle Scholar
  11. 11.
    Dubois, Y., Prade, H.: Fuzzy Sets and Systems-Theory and Applications. Academic Press, New York (1980)MATHGoogle Scholar
  12. 12.
    Qihe, L., Fan, L., Fan, M.: An efficient knowledge reduction algorithm based on new conditional information entropy. Control and Decision 20(8), 878–882 (2005)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Qihe Liu
    • 1
  • Leiting Chen
    • 1
  • Jianzhong Zhang
    • 1
  • Fan Min
    • 1
  1. 1.College of Computer Science and EngineeringUniversity of Electronic Science and, Technology of ChinaChengduChina

Personalised recommendations