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Decision Table Reduction in KDD: Fuzzy Rough Based Approach

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Transactions on Rough Sets XI

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 5946))

Abstract

Decision table reduction in KDD refers to the problem of selecting those input feature values that are most predictive of a given outcome by reducing a decision table like database from both vertical and horizontal directions. Fuzzy rough sets has been proven to be a useful tool of attribute reduction (i.e. reduce decision table from vertical direction). However, relatively less researches on decision table reduction using fuzzy rough sets has been performed. In this paper we focus on decision table reduction with fuzzy rough sets. First, we propose attribute-value reduction with fuzzy rough sets. The structure of the proposed value-reduction is then investigated by the approach of discernibility vector. Second, a rule covering system is described to reduce the valued-reduced decision table from horizontal direction. Finally, numerical example illustrates the proposed method of decision table reduction. The main contribution of this paper is that decision table reduction method is well combined with knowledge representation of fuzzy rough sets by fuzzy rough approximation value. The strict mathematical reasoning shows that the fuzzy rough approximation value is the reasonable criterion to keep the information invariant in the process of decision table reduction.

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References

  1. Bezdek, J.C., Harris, J.O.: Fuzzy partitions and relations: an axiomatic basis of clustering. Fuzzy Sets and Systems 84, 143–153 (1996)

    Article  MathSciNet  Google Scholar 

  2. Bhatt, R.B., Gopal, M.: On fuzzy rough sets approach to feature selection. Pattern recognition Letters 26, 1632–1640 (2005)

    Article  Google Scholar 

  3. Cattaneo, G.: Fuzzy extension of rough sets theory. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 275–282. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  4. Degang, C., Wenxiu, Z., Yeung, D.S., Tsang, E.C.C.: Rough approximations on a complete completely distributive lattice with applications to generalized rough sets. Information Sciences 176, 1829–1848 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chen, D.G., Wang, X.Z., Zhao, S.Y.: Attribute Reduction Based on Fuzzy Rough Sets. In: Kryszkiewicz, M., Peters, J.F., Rybiński, H., Skowron, A. (eds.) RSEISP 2007. LNCS (LNAI), vol. 4585, pp. 381–390. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Cornelis, C., De Cock, M., Radzikowska, A.M.: Fuzzy rough sets: from theory into practice. In: Pedrycz, W., Skowron, A., Kreinovich, V. (eds.) Handbook of Granular Computing. Springer, Heidelberg (in press)

    Google Scholar 

  7. Devijver, P., Kittler, J.: Pattern Recognition: A Statistical Approach. Prentice Hall, Englewood Cliffs (1982)

    MATH  Google Scholar 

  8. Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Internat. J. Genaral Systems 17(2-3), 191–209 (1990)

    Article  MATH  Google Scholar 

  9. Dubois, D., Prade, H.: Putting rough sets and fuzzy sets together, Intelligent Decision support. In: Slowinski, R. (ed.) Handbook of applications and advances of the rough sets theory. Kluwer Academic Publishers, Dordrecht (1992)

    Google Scholar 

  10. Fernandez Salido, J.M., Murakami, S.: Rough set analysis of a general type of fuzzy data using transitive aggregations of fuzzy similarity relations. Fuzzy Sets and Systems 139, 635–660 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Greco, S., Inuiguchi, M., Slowinski, R.: A new proposal for fuzzy rough approximations and gradual decision rule representation. In: Peters, J.F., Skowron, A., Dubois, D., Grzymała-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds.) Transactions on Rough Sets II. LNCS, vol. 3135, pp. 319–342. Springer, Heidelberg (2004)

    Google Scholar 

  12. Hu, Q.H., Yu, D.R., Xie, Z.X.: Information-preserving hybrid data reduction based on fuzzy-rough techniques. Pattern Recognition Letters 27, 414–423 (2006)

    Article  Google Scholar 

  13. Hong, T.P.: Learning approximate fuzzy rules from training examples. In: The proceeding of the Tenth IEEE International Conference on Fuzzy Systems, Melbourne, Australia, vol. 1, pp. 256–259 (2001)

    Google Scholar 

  14. Jensen, R., Shen, Q.: Fuzzy-rough attribute reduction with application to web categorization. Fuzzy Sets and Systems 141, 469–485 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  15. Mi, J.S., Zhang, W.X.: An axiomatic characterization of a fuzzy generalization of rough sets. Information Sciences 160(1-4), 235–249 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  16. Morsi, N.N., Yakout, M.M.: Axiomatics for fuzzy rough sets. Fuzzy Sets and Systems 100(1998), 327–342 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  17. Pawlak, Z.: Rough Sets Internat. J. Comput. Inform. Sci. 11(5), 341–356 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  18. Radzikowska, A.M., Kerre, E.E.: A comparative study of fuzzy rough sets. Fuzzy Sets and Systems 126, 137–155 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems, Intelligent Decision support. In: Slowinski, R. (ed.) Handbook of applications and advances of the rough sets theory. Kluwer Academic Publishers, Dordrecht (1992)

    Google Scholar 

  20. Skowron, A., Polkowski, L.: Rough sets in knowledge discovery, vol. 1,2. Springer, Berlin (1998)

    Google Scholar 

  21. Slowinski, R. (ed.): Intelligent decision support: Handbook of applications and advances of the rough sets theory. Kluwer Academic Publishers, Dordrecht (1992)

    MATH  Google Scholar 

  22. Slowinski, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations. In: Wang, P.P. (ed.) Advances in Machine Intelligence and Soft-Computing, Department of Electrical Engineering, Duke University, Durham, NC, USA, pp. 17–33 (1997)

    Google Scholar 

  23. Sudkamp, T.: Similarity, interpolation, and fuzzy rule construction. Fuzzy Sets and Systems 58, 73–86 (1993)

    Article  MathSciNet  Google Scholar 

  24. Tsang, E.C.C., Chen, D.G., Yeung, D.S., Wang, X.Z., Lee, J.W.T.: Attributes reduction using fuzzy rough sets. IEEE Transaction on Fuzzy System (in press)

    Google Scholar 

  25. Tsai, Y.-C., Cheng, C.-H., Chang, J.-R.: Entropy-based fuzzy rough classification approach for extracting classification rules. Expert Systems with Applications 31(2), 436–443 (2006)

    Article  Google Scholar 

  26. Wang, X.Z., Hong, J.R.: Learning optimization in simplifying fuzzy rules. Fuzzy Sets and Systems 106, 349–356 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  27. Wang, X.Z., Tsang, E.C.C., Zhao, S.Y., Chen, D.G., Yeung, D.S.: Learning Fuzzy Rules from Fuzzy Samples Based on Rough Set Technique. Information Sciences 177(20), 4493–4514 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  28. Wu, W.Z., Mi, J.S., Zhang, W.X.: Generalized fuzzy rough sets. Information Sciences 151, 263–282 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  29. Wu, W.Z., Zhang, W.X.: Constructive and axiomatic approaches of fuzzy approximation operators. Information Sciences 159(3-4), 233–254 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  30. Yasdi, R.: Learning classification rules from database in the context of knowledge acquisition and representation. IEEE transaction on knowledge and data engineering 3(3), 293–306 (1991)

    Article  Google Scholar 

  31. Yao, Y.Y.: Combination of rough and fuzzy sets based on level sets. In: Lin, T.Y., Cercone, N. (eds.) Rough Sets and Data mining: Analysis for Imprecise Data, pp. 301–321. Kluwer Academic Publishers, Boston (1997)

    Google Scholar 

  32. Yeung, D.S., Chen, D.G., Tsang, E.C.C., Lee, J.W.T.: On the Generalization of Fuzzy Rough Sets. IEEE Transactions on Fuzzy Systems 13, 343–361 (2005)

    Article  Google Scholar 

  33. Zhao, S., Tsang, E.C.C.: The Analysis of Attribute Reduction on Fuzzy Rough Sets: the T-norm and Fuzzy Approximation Operator Perspective. Submitted to information science special issue

    Google Scholar 

  34. Ziarko, W.P. (ed.): Rough sets, fuzzy sets and knowledge discovery, Workshop in Computing. Springer, London (1994)

    Google Scholar 

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Tsang, E., Suyun, Z. (2010). Decision Table Reduction in KDD: Fuzzy Rough Based Approach. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets XI. Lecture Notes in Computer Science, vol 5946. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11479-3_10

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  • DOI: https://doi.org/10.1007/978-3-642-11479-3_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11478-6

  • Online ISBN: 978-3-642-11479-3

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