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Characteristic Relations for Incomplete Data: A Generalization of the Indiscernibility Relation

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3700)

Abstract

This paper shows that attribute-value pair blocks, used for many years in rule induction, may be used as well for computing indiscernibility relations for completely specified decision tables. Much more importantly, for incompletely specified decision tables, i.e., for data with missing attribute values, the same idea of attribute-value pair blocks is a convenient tool to compute characteristic sets, a generalization of equivalence classes of the indiscernibility relation, and also characteristic relations, a generalization of the indiscernibility relation. For incompletely specified decision tables there are three different ways lower and upper approximations may be defined: singleton, subset and concept. Finally, it is shown that, for a given incomplete data set, the set of all characteristic relations for the set of all congruent decision tables is a lattice.

Keywords

Characteristic Relation Decision Table Rule Induction Indiscernibility Relation Rule Induction Algorithm 
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.
    Birkhoff, G.: Lattice Theory. American Mathematical Society, Providence, RI (1940)Google Scholar
  2. 2.
    Greco, S., Matarazzo, S.B., Slowinski, R.: Dealing with missing data in rough set analysis of multi-attribute and multi-criteria decision problems. In: Zanakis, S.H., Doukidis, G., Zopounidis, Z. (eds.) Decision Making: Recent developments and Worldwide Applications, pp. 295–316. Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
  3. 3.
    Grzymala-Busse, J.W.: On the unknown attribute values in learning from examples. In: Raś, Z.W., Zemankova, M. (eds.) ISMIS 1991. LNCS(LNAI), vol. 542, pp. 368–377. Springer, Heidelberg (1991)Google Scholar
  4. 4.
    Grzymala-Busse, J.W.: LERS—A system for learning from examples based on rough sets. In: Slowinski, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory, pp. 3–18. Kluwer Academic Publishers, Dordrecht (1992)Google Scholar
  5. 5.
    Grzymala-Busse, J.W.: Rough set strategies to data with missing attribute values. In: Workshop Notes, Foundations and New Directions of Data Mining, the 3-rd International Conference on Data Mining, Melbourne, FL, USA, November 19-22, pp. 56–63 (2003)Google Scholar
  6. 6.
    Grzymała-Busse, J.W.: Characteristic relations for incomplete data: A generalization of the indiscernibility relation. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 244–253. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Grzymała-Busse, J.W., Hu, M.: A comparison of several approaches to missing attribute values in data mining. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 340–347. Springer, Heidelberg (2001)Google Scholar
  8. 8.
    Grzymala-Busse, J.W., Wang, A.Y.: Modified algorithms LEM1 and LEM2 for rule induction from data with missing attribute values. In: Proc. of the Fifth International Workshop on Rough Sets and Soft Computing (RSSC 1997) at the Third Joint Conference on Information Sciences (JCIS 1997), Research Triangle Park, NC, March 2-5, pp. 69–72 (1997)Google Scholar
  9. 9.
    Kryszkiewicz, M.: Rough set approach to incomplete information systems. In: Proceedings of the Second Annual Joint Conference on Information Sciences, Wrightsville Beach, NC, September 28-October 1, pp. 194–197 (1995)Google Scholar
  10. 10.
    Kryszkiewicz, M.: Rules in incomplete information systems. Information Sciences 113, 271–292 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Pawlak, Z.: Rough Sets. In: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)Google Scholar
  13. 13.
    Slowinski, R., Vanderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE Transactions on Knowledge and Data Engineering 12, 331–336 (2000)CrossRefGoogle Scholar
  14. 14.
    Stefanowski, J.: Algorithms of Decision Rule Induction in Data Mining. Poznan University of Technology Press, Poznan (2001)Google Scholar
  15. 15.
    Stefanowski, J., Tsoukiàs, A.: On the extension of rough sets under incomplete information. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 73–81. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  16. 16.
    Stefanowski, J., Tsoukias, A.: Incomplete information tables and rough classification. Computational Intelligence 17, 545–566 (2001)CrossRefGoogle Scholar
  17. 17.
    Yao, Y.Y.: Two views of the theory of rough sets in finite universes. International J. of Approximate Reasoning 15, 291–317 (1996)zbMATHCrossRefGoogle Scholar
  18. 18.
    Yao, Y.Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences 111, 239–259 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Yao, Y.Y.: On the generalizing rough set theory. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 44–51. Springer, Heidelberg (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of Electrical Engineering and Computer ScienceUniversity of KansasLawrenceUSA
  2. 2.Institute of Computer SciencePolish Academy of SciencesWarsawPoland

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