Consistency and Fuzziness in Ordered Decision Tables

  • Yuhua Qian
  • Jiye Liang
  • Wei Wei
  • Feng Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5009)


In this paper, we focus on how to measure the consistency of an ordered decision table and the fuzziness of an ordered rough set and an ordered rough classification in the context of ordered information systems. The membership function of an object is defined through using the dominance class including itself. Based on the membership function, we introduce a consistency measure to assess the consistency of an ordered decision table and define two fuzziness measures to compute the fuzziness of an ordered rough set and an ordered rough classification. Several examples are employed to illustrate their mechanisms as well. These results will be helpful for understanding the uncertainty in ordered information systems and ordered decision tables.


Ordered decision table Consistency Fuzziness 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data, System Theory, Knowledge Engineering and Problem Solving. Kluwer, Dordrecht (1991)Google Scholar
  2. 2.
    Pawlak, Z., Skowron, A.: Rudiments of Rough Sets. Information Sciences 177, 3–27 (2007)CrossRefMathSciNetzbMATHGoogle Scholar
  3. 3.
    Dubois, D., Prade, H.: Rough Fuzzy Sets and Fuzzy Rough Sets. International Journal of General Systems 17, 191–209 (1990)CrossRefzbMATHGoogle Scholar
  4. 4.
    Düntsch, I., Gediga, G.: Uncertainty Measures of Rough Set Prrediction. Artificial Intelligence 106, 109–137 (1998)CrossRefMathSciNetzbMATHGoogle Scholar
  5. 5.
    Gediga, G., Düntsch, I.: Rough Approximation Quality Revisited. Artificial Intelligence 132, 219–234 (2001)CrossRefzbMATHGoogle Scholar
  6. 6.
    Jensen, R., Shen, Q.: Fuzzy-rough Sets assisted Attribute Selection. IEEE Transactions on Fuzzy Systems 15(1), 73–89 (2007)CrossRefGoogle Scholar
  7. 7.
    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. International Journal of General Systems 31(4), 331–342 (2002)CrossRefMathSciNetzbMATHGoogle Scholar
  8. 8.
    Qian, Y.H., Liang, J.Y.: Rough Set Method Based on Multi-granulations. In: 5th IEEE Conference on Cognitive Informatics I, pp. 297–304 (2006)Google Scholar
  9. 9.
    Guan, J.W., Bell, D.A.: Rough Computational Methods for Information Systems. Artificial Intelligence 105, 77–103 (1998)CrossRefzbMATHGoogle Scholar
  10. 10.
    Jeon, G., Kim, D., Jeong, J.: Rough Sets Attributes Reduction Based Expert System in Interlaced Video. IEEE Transactions on Consumer Electronics 52(4), 1348–1355 (2006)CrossRefGoogle Scholar
  11. 11.
    Kryszkiewicz, M.: Rough Set Approach to Incomplete Information Systems. Information Sciences 112, 39–49 (1998)CrossRefMathSciNetzbMATHGoogle Scholar
  12. 12.
    Liang, J.Y., Li, D.Y.: Uncertainty and Knowledge Acquisition in Information Systems. Science Press, Beijing (2005)Google Scholar
  13. 13.
    Liang, J.Y., Qian, Y.H.: Axiomatic Approach of Knowledge Granulation in Information Systems. In: Sattar, A., Kang, B.-h. (eds.) AI 2006. LNCS (LNAI), vol. 4304, pp. 1074–1078. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Qian, Y.H., Liang, J.Y.: Combination Entropy and Combination Granulation in Incomplete Information Systems. In: Wang, G.-Y., Peters, J.F., Skowron, A., Yao, Y. (eds.) RSKT 2006. LNCS (LNAI), vol. 4062, pp. 184–190. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Greco, S., Matarazzo, B., Slowinski, R.: Rough Sets Theory for Multicriteria Decision Analysis. European Journal of Operational Research 129, 11–47 (2001)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Greco, S., Matarazzo, B., Slowinski, R.: Rough sets Methodology for Sorting Problems in Presense of Multiple Attributes and Criteria. European Journal of Operational Research 138, 247–259 (2002)CrossRefMathSciNetzbMATHGoogle Scholar
  17. 17.
    Qian, Y.H., Liang, J.Y.: Evaluation Method for Decision Rule Sets. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds.) RSFDGrC 2007. LNCS (LNAI), vol. 4482, pp. 272–279. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  18. 18.
    Qian, Y.H., Liang, J.Y., Li, D.Y., Zhang, H.Y., Dang, C.Y.: Measures for Evaluating the Decision Performance of a Decision Table in Rough Set Theory. Information Sciences 178(1), 181–202 (2008)CrossRefzbMATHGoogle Scholar
  19. 19.
    Qian, Y.H., Liang, J.Y., Dang, C.Y., Zhang, H.Y., Ma, J.M.: On the Evaluation of the Decision Performance of an Incomplete Decision Table. Data and Knowledge Engineering. doi:10.1016/j.datak.2007.12.002.Google Scholar
  20. 20.
    Shao, M.W., Zhang, W.X.: Dominance Relation and Rules in an Incomplete Ordered Information System. International Journal of Intelligent Systems 20, 13–27 (2005)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Yuhua Qian
    • 1
  • Jiye Liang
    • 1
  • Wei Wei
    • 1
  • Feng Wang
    • 1
  1. 1.Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of EducationTaiyuanChina

Personalised recommendations