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Structure-Based Attribute Reduction: A Rough Set Approach

Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 584)

Abstract

We provide an introduction to a rough set approach to attribute reduction. Analyzed data sets consist of objects which are described by attributes and partitioned into decision classes. Rough set theory deals with uncertainty decision classes with respect to attributes by approximating them to precise sets. The aim of attribute reduction is to remove redundant attributes as well as find important ones for classification. Several types of attribute reduction have been proposed especially according to preserving structures of approximated decision classes. We introduce definitions and theoretical results about structures-based attribute reduction.

Keywords

Rough set model Reduct Boolean function Structure-based reduct 

References

  1. 1.
    Bazan, J.G., Nguyen, H.S., Nguyen, S.H., Synak, P., Wróblewski, J.: Rough set algorithms in classification problem. In: Polkowski, L., Tsumoto, S., Lin, T.Y. (eds.) Rough Set Methods and Applications, pp. 49–88. Physica-Verlag, New York (2000)CrossRefGoogle Scholar
  2. 2.
    Ben-David, A.: Monotonicity maintenance in information-theoretic machine learning algorithms. Mach. Learn. 19, 29–43 (1995)Google Scholar
  3. 3.
    Ben-David, A., Sterling, L., Pao, Y.H.: Learning and classification of monotonic ordinal concepts. Comput. Intell. 5(1), 45–49 (1989)CrossRefGoogle Scholar
  4. 4.
    Beynon, M.: Reducts within the variable precision rough sets model: a further investigation. Eur. J. Oper. Res. 134(3), 592–605 (2001)CrossRefMATHGoogle Scholar
  5. 5.
    Beynon, M.J., Peel, M.J.: Variable precision rough set theory and data discretisation: an application to corporate failure prediction. Omega 29, 561–576 (2001)CrossRefGoogle Scholar
  6. 6.
    Chen, D., Hu, Q., Yang, Y.: Parameterized attribute reduction with Gaussian kernel based fuzzy rough sets. Inf. Sci. 181, 5169–5179 (2011)CrossRefMATHGoogle Scholar
  7. 7.
    Chmielewski, M.R., Grzymala-Busse, J.W.: Global discretization of continuous attributes as preprocessing for machine learning. Int. J. Approx. Reason. 15, 319–331 (1996)CrossRefMATHGoogle Scholar
  8. 8.
    Cornelis, C., Jensen, R., Hurtado, G., Ślȩzak, D.: Attribute selection with fuzzy decision reducts. Inf. Sci. 180, 209–224 (2010)CrossRefMATHGoogle Scholar
  9. 9.
    Crama, Y., Hammer, P.L.: Boolean Functions: Theory, Algorithms, and Applications. Cambridge University Press, New York (2011)CrossRefGoogle Scholar
  10. 10.
    Dembczyński, K., Greco, S., Kotłowski, W., Słowiński, R.: Quality of rough approximation in multi-criteria classification problems. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) 5th International Conference on Rough Sets and Current Trends in Computing, RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 318–327. Springer, Heidelberg (2006)Google Scholar
  11. 11.
    Dimitras, A.I., Slowinski, R., Susmaga, R., Zopounidis, C.: Business failure prediction using rough sets. Eur. J. Oper. Res. 114, 263–280 (1999)CrossRefMATHGoogle Scholar
  12. 12.
    Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 17(2–3), 191–209 (1990)Google Scholar
  13. 13.
    Düntsch, I., Gediga, G.: Uncertainty measures of rough set prediction. Artif. Intell. 106, 109–137 (1998)CrossRefMATHGoogle Scholar
  14. 14.
    Eiter, T., Makino, K., Gottlob, G.: Computational aspects of monotone dualization: a brief survey. Discret. Appl. Math. 156, 2035–2049 (2011)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Fayyad, U.M., Irani, K.B.: On the handling of continuous-valued attributes in decision tree generation. Mach. Learn. 8(1), 87–102 (1992)MATHGoogle Scholar
  16. 16.
    Greco, S., Matarazzo, B., Slowinski, R.: Rough set theory for multicriteria decision analysis. Eur. J. Oper. Res. 129(1), 1–47 (2001)CrossRefMathSciNetMATHGoogle Scholar
  17. 17.
    Greco, S., Matarazzo, B., Slowinski, R.: Multicriteria classification by dominance-based rough set approach. In: Kloesgen, W., Zytkow, J.M. (eds.) Handbook of Data Mining and Knowledge Discovery. Oxford University Press, New York (2002)Google Scholar
  18. 18.
    Greco, S., Matarazzo, B., Słowiński, R.: Decision rule approach. In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multiple Criteria Decision Analysis: State of the Surveys, pp. 507–561. Springer, New York (2005)Google Scholar
  19. 19.
    Hassanien, A.E.: Rough set approach for attribute reduction and rule generation: a case of patients with suspected breast cancer. J. Am. Soc. Inf. Sci. Technol. 55(11), 954–962 (2004)CrossRefGoogle Scholar
  20. 20.
    Inuiguchi, M.: Attribute reduction in variable precision rough set model. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 14(4), 461–479 (2006)CrossRefMathSciNetMATHGoogle Scholar
  21. 21.
    Inuiguchi, M.: Structure-based attribute reduction in variable precision rough set models. J. Adv. Comput. Intell. Intell. Inf. 10(5), 657–665 (2006)MathSciNetGoogle Scholar
  22. 22.
    Inuiguchi, M., Tanino, T.: New fuzzy rough sets based on certainty qualification. In: Pal, S.K., Polkowski, L., Skowron, A. (eds.) Rough-Neural Computing: Techniques for Computing with Words, pp. 277–296. Springer, Berlin (2004)CrossRefGoogle Scholar
  23. 23.
    Inuiguchi, M., Tsurumi, M.: Measures based on upper approximations of rough sets for analysis of attribute importance and interaction. Int. J. Innov. Comput. Inf. Control 2(1), 1–12 (2006)Google Scholar
  24. 24.
    Inuiguchi, M., Matsumoto, Y.: Refinement of attribute reduction in the classical rough sets toward decision analysis. In: International Workshop on Soft Computing for Knowledge Technology (2008)Google Scholar
  25. 25.
    Inuiguchi, M., Yoshioka, Y.: Several reducts in dominance-based rough set approach. In: Huynh, V.N., Nakamori, Y., Ono, H., Lawry, J., Kreinovich, V., Nguyen, H.T. (eds.) Interval/Probabilistic Uncertainty and Non-classical Logics. Advances in Soft Computing, vol. 46, pp. 163–175. Springer, Berlin (2008)CrossRefGoogle Scholar
  26. 26.
    Inuiguchi, M., Yoshioka, Y., Kusunoki, Y.: Variable-precision dominance-based rough set approach and attribute reduction. Int. J. Approx. Reason. 50(8), 1199–1214 (2009)CrossRefMathSciNetMATHGoogle Scholar
  27. 27.
    Jensen, R., Shen, Q.: Semantics-preserving dimensionality reduction: rough and fuzzy-rough-based approaches. IEEE Trans. Knowl. Data Eng. 16(12), 1457–1471 (2004)CrossRefGoogle Scholar
  28. 28.
    Jensen, R., Tuson, A., Shen, Q.: Finding rough and fuzzy-rough set reducts with SAT. Inf. Sci. 255, 100–120 (2014)CrossRefMathSciNetGoogle Scholar
  29. 29.
    Kryszkiewicz, M.: Rough set approach to incomplete information systems. Inf. Sci. 112, 39–49 (1998)CrossRefMathSciNetMATHGoogle Scholar
  30. 30.
    Kryszkiewicz, M.: Comparative study of alternative types of knowledge reduction in inconsistent systems. Int. J. Intell. Syst. 16, 105–120 (2001)CrossRefMATHGoogle Scholar
  31. 31.
    Kusunoki, Y., Inuiguchi, M.: A unified approach to reducts in dominance-based rough set approach. Soft Comput. 14, 507–515 (2010)CrossRefMATHGoogle Scholar
  32. 32.
    Lievens, S., Baets, B.D., Cao-Van, K.: A probabilistic framework for the design of instance-based supervised ranking algorithms in an ordinal setting. Ann. Oper. Res. 163, 115–142 (2008)CrossRefMathSciNetMATHGoogle Scholar
  33. 33.
    Mi, J., Wu, W., Zhang, W.: Approaches to knowledge reduction based on variable precision rough set model. Inf. Sci. 159, 255–272 (2004)CrossRefMathSciNetMATHGoogle Scholar
  34. 34.
    Nguyen, L.G., Nguyen, H.S.: On elimination of redundant attributes in decision tables. In: Proceedings of the Federated Conference on Computer Science and Information Systems, pp. 317–322 (2012)Google Scholar
  35. 35.
    Pawlak, Z.: Rough sets. Int. J. Inf. Comput. Sci. 11(5), 341–356 (1982)CrossRefMathSciNetMATHGoogle Scholar
  36. 36.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)CrossRefMATHGoogle Scholar
  37. 37.
    Pawlak, Z., Skowron, A.: Rough sets and boolean reasoning. Inf. Sci. 177, 41–73 (2007)CrossRefMathSciNetMATHGoogle Scholar
  38. 38.
    Pawlak, Z., Skowron, A.: Rough sets: some extensions. Inf. Sci. 177, 28–40 (2007)CrossRefMathSciNetMATHGoogle Scholar
  39. 39.
    Pawlak, Z., Skowron, A.: Rudiments of rough sets. Inf. Sci. 177, 3–27 (2007)CrossRefMathSciNetMATHGoogle Scholar
  40. 40.
    Pawlak, Z., Słowiński, R.: Rough set approach to multi-attribute decision analysis. Eur. J. Oper. Res. 72, 443–459 (1994)CrossRefMATHGoogle Scholar
  41. 41.
    Sawicki, P., Żak, J.: Technical diagnostic of a fleet of vehicles using rough set theory. Eur. J. Oper. Res. 193, 891–903 (2009)CrossRefMATHGoogle Scholar
  42. 42.
    Shen, Q., Jensen, R.: Rough sets, their extensions and applications. Int. J. Autom. Comput. 4(3), 217–228 (2007)CrossRefGoogle Scholar
  43. 43.
    Skowron, A., Rauszer, C.: The discernibility matrix and function in information systems. In: Słowiński, R. (ed.) Intelligent Decision Support: Handbook of Application and Advances of Rough Set Theory, pp. 331–362. Kluwer Academic Publishers, Dordrecht (1992)CrossRefGoogle Scholar
  44. 44.
    Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundam. Inform. 27(2–3), 245–253 (1996)MathSciNetMATHGoogle Scholar
  45. 45.
    Ślȩzak, D.: Various approaches to reasoning with frequency based decision reducts: a survey. In: Polkowski, L., Tsumoto, S., Lin, T.Y. (eds.) Rough Set Methods and Applications, pp. 235–285. Physica-Verlag, New York (2000)Google Scholar
  46. 46.
    Ślȩzak, D.: Approximate entropy reducts. Fundam. Inform. 53, 365–390 (2002)Google Scholar
  47. 47.
    Ślȩzak, D., Ziarko, W.: The investigation of the Bayesian rough set model. Int. J. Approx. Reason. 40, 81–91 (2005)CrossRefGoogle Scholar
  48. 48.
    Ślȩzak, D., Janusz, A.: Ensembles of bireducts: towards robust classification and simple representation. In: Kim, T.H., Adeli, H., Slezak, D., Sandnes, F.E., Song, X., Chung, K.I., Arnett, K.P. (eds.) Future Generation Information Technology: Third International Conference, FGIT 2011. LNCS, vol. 7105, pp. 64–77. Springer, Berlin (2011)CrossRefGoogle Scholar
  49. 49.
    Susmaga, R., Słowiński, R., Greco, S., Matarazzo, B.: Generation of reducts and rules in multi-attribute and multi-criteria classification. Control Cybern. 29(4), 969–988 (2000)MATHGoogle Scholar
  50. 50.
    Swiniarski, R.W., Skowron, A.: Rough set methods in feature selection and recognition. Pattern Recognit. Lett. 24, 833–849 (2003)CrossRefMATHGoogle Scholar
  51. 51.
    Wróblewski, J.: Ensembles of classifiers based on approximate reducts. Fundam. Inform. 47, 351–360 (2001)MATHGoogle Scholar
  52. 52.
    Yang, X., Yang, J., Wu, C., Yu, D.: Dominance-based rough set approach and knowledge reductions in incomplete ordered information system. Inf. Sci. 178, 1219–1234 (2008)CrossRefMathSciNetMATHGoogle Scholar
  53. 53.
    Ziarko, W.: Variable precision rough set model. J. Comput. Syst. Sci. 46(1), 39–59 (1993)CrossRefMathSciNetMATHGoogle Scholar
  54. 54.
    Ziarko, W.: Probabilistic approach to rough sets. Int. J. Approx. Reason. 49, 272–284 (2008)CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Graduate School of EngineeringOsaka UniversitySuita, OsakaJapan
  2. 2.Graduate School of Engineering SciencesOsaka UniversityToyonaka, OsakaJapan

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