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Expansions of Rough Sets in Incomplete Information Systems

  • Xibei Yang
  • Jingyu Yang

Abstract

Generally speaking, an incomplete information system indicates a system with unknown values. In this chapter, several expanded rough sets approaches to incomplete information system have been introduced. Firstly, by assuming that the unknown values can be compared with any values in the domains of the corresponding attributes, the tolerance relation, valued tolerance relation, maximal consistent block, descriptor can be used to construct rough approximations, respectively. Secondly, by assuming that the unknown values cannot be compared with any values in the domains of the corresponding attributes, the similarity relation, difference relation can be used to construct rough approximations, respectively. Finally, by considering the above two different semantic explanations of the unknown values, the characteristic relation can be used to construct rough approximation.

Keywords

Negative Rule Tolerance Relation Decision Class Consistent Attribute Approximate Distribution 
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.

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References

  1. [1]
    Gore, A.: Earth in the balance. New York: Plume Books (1992)Google Scholar
  2. [2]
    Ebenbach, D. H., Moore, C. F.: Incomplete information, inferences, and individual differences: the case of environmental judgements. Organ. Behav. Hum. Dec. 81, 1–27 (2000)CrossRefGoogle Scholar
  3. [3]
    Grzymala-Busse, J.W., Rząsa, W.: Local and global approximations for incomplete data. Transactions on Rough Sets VIII, LNCS, 5084, 21–34 (2008)CrossRefGoogle Scholar
  4. [4]
    Hong, T. P., Tseng, L. H., Wang, S. L.: Learning rules from incomplete training examples by rough sets. Expert Syst. Appl. 22, 285–293 (2002)CrossRefGoogle Scholar
  5. [5]
    Kryszkiewicz, M.: Rough set approach to incomplete information systems. In: Proceedings of the Second Annual Joint Conference on Information Sciences, pp. 194–197 (1995)Google Scholar
  6. [6]
    Kryszkiewicz, M.: Rough set approach to incomplete information systems. Informa. Sci. 112, 39–49 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    Kryszkiewicz, M.: Rules in incomplete information systems. Inform. Sci. 113, 271–292 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    Latkowski, R.: On Decomposition for incomplete data. Fund. Informa. 54, 1–16 (2003)MathSciNetzbMATHGoogle Scholar
  9. [9]
    Latkowski, R.: Flexible indiscernibility relations for missing attribute values. Fund. Inform. 67, 131–147 (2005)MathSciNetzbMATHGoogle Scholar
  10. [10]
    Liang J. Y., Shi, Z. Z., Li, D. Y., Wierman, M. J.: Information entropy, rough entropy and knowledge granulation in incomplete information systems. Int. J. Gen. Syst. 35, 641–654 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    Nakamura, A.: A rough logic aased on incomplete information and its application. Int. J. Approx. Reason. 15, 367–378 (1995)CrossRefGoogle Scholar
  12. [12]
    Qian, Y. H., Liang, J. Y., Pedrycz, W., Dang, C. Y.: An effcient accelerator for attribute reduction from incomplete data in rough set framework. Pattern Recognit. 44, 1658–1670 (2011)zbMATHCrossRefGoogle Scholar
  13. [13]
    Salama, A. S.: Topological solution of missing attribute values problem in incomplete information tables. Inform. Sci. 180, 631–639 (2010)MathSciNetCrossRefGoogle Scholar
  14. [14]
    Wu, W. Z.: Attribute reduction based on evidence theory in incomplete decision systems. Inform. Sci. 178, 1355–1371 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    Wu, C., Wang, L. J.: An improved limited and variable precision rough set model for rule acquisition based on pansystems methodology. Kybernetes. 37, 1264–1271 (2008)zbMATHCrossRefGoogle Scholar
  16. [16]
    Wu, W. Z., Zhang, W. X., Li, H. Z.: Knowledge acquisition in incomplete fuzzy information systems via the rough set approach. Expert Syst. 20, 280–286 (2003)CrossRefGoogle Scholar
  17. [17]
    Yang, X. P.: Fuzziness in incomplete information systems. In: Proceedmgs of the Third International Conference on Machine Learning and Cybemetics, pp. 1599–1603 (2004)Google Scholar
  18. [18]
    Yang, X. B., Qu, F., Yang, J. Y., Xie J.: A novel extension of rough set model in incomplete information system. In: Third International Conference on Innovative Computing, Information and Control, pp. 306–306 (2008)Google Scholar
  19. [19]
    Zhang, W. X., Mi, J. S.: Incomplet information system and its optimal selections. Comput. Math. Appl. 48, 691–698 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  20. [20]
    Wang, G. Y.: Extension of rough set under incomplete information systems. In: Proceeding of the 11th IEEE International Conference on Fuzzy Systems, pp. 1098–1103 (2002)Google Scholar
  21. [21]
    Wang, G. Y., Guan L. H., Hu F.: Rough set extensions in incomplete information systems. Front. Electr. Electron. Eng. China, 3, 399–405 (2008)zbMATHCrossRefGoogle Scholar
  22. [22]
    Grzymala-Busse, J. W.: On the unknown attribute values in learning from examples. In: Proceeding of the Sixth International Symposium on Methodologies for Intelligent Systems, pp. 368–377 (1991)Google Scholar
  23. [23]
    Grzymala-Busse, J. W.: Characteristic relations for incomplete data: A generalization of the indiscernibility relation. In: Proceeding of the Third International Conference on Rough Sets and Current Trends in Computing, pp. 244–253 (2004)Google Scholar
  24. [24]
    Grzymala-Busse, J. W.: Data with missing attribute values: Generalization of indiscernibility relation and rule reduction. Transactions on Rough Sets I, LNCS, 3100, 78–95 (2004)CrossRefGoogle Scholar
  25. [25]
    Grzymala-Busse, J. W., Wang, A. Y.: Modified algorithms LEM1 and LEM2 for rule induction from data with missing attribute values. In: Proceeding of the Fifth International Workshop on Rough Sets and Soft Computing at the Third Joint Conference on Information Sciences, pp. 69–72 (1997)Google Scholar
  26. [26]
    Stefanowski, J., Tsoukiàs, A.: On the extension of rough sets under incomplete information. In: Proceeding of New directions in rough sets, data mining and granular-soft computing, pp. 73–82 (1999)Google Scholar
  27. [27]
    Stefanowski, J., Tsoukiàs, A.: Incomplete information tables and rough classification. Comput. Intell. 17, 545–566 (2001)CrossRefGoogle Scholar
  28. [28]
    Guan, Y. Y., Wang, H. K.: Set-valued information systems. Inform. Sci. 176, 2507–2525 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  29. [29]
    Leung, Y., Li, D. Y.: Maximal consistent block technique for rule acquisition in incomplete information systems. Inform. Sci. 115, 85–106 (2003)MathSciNetCrossRefGoogle Scholar
  30. [30]
    Qian, Y. H., Liang, J. Y., Li, D. Y., Wang, F., Ma, N. N.: Approximation reduction in inconsistent incomplete decision tables. Knowl.-Based Syst. 23, 427–433 (2010)CrossRefGoogle Scholar
  31. [31]
    Leung, Y., Wu, W. Z., Zhang, W. X.: Knowledge acquisition in incomplete information systems: a rough set approach. Eur. J. Oper. Res. 168, 464–473 (2006)MathSciNetGoogle Scholar
  32. [32]
    Wu, W. Z., Xu, Y. H.: On two types of generalized rough set approximations in incomplete information systems. In: 2005 IEEE International Conference on Granular Computing, pp. 303–306 (2005)Google Scholar
  33. [33]
    Tsumoto, S.: Automated discovery of positive and negative knowledge in clinical databases, IEEE Eng. Med. Biol. 19, 56–62 (2000)CrossRefGoogle Scholar
  34. [34]
    Tsumoto, S.: Automated extraction of medical expert system rules from clinical databases on rough set theory. Inform. Sci. 112, 67–84 (1998)CrossRefGoogle Scholar
  35. [35]
    Yang, X. B., Yu, D. J., Yang J. Y., Song, X. N.: Difference relation-based rough set and negative rrules in incomplete information system. Int. J. Uncertain. Fuzz. 17, 649–665 (2009)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Science Press Beijing and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Xibei Yang
    • 1
  • Jingyu Yang
    • 2
  1. 1.School of Computer Science and EngineeringJiangsu University of Science and TechnologyZhenjiang JiangsuP.R. China
  2. 2.School of Computer Science and TechnologyNanjing University of Science and TechnologyNanjing JiangsuP.R. China

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