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Universal Problem of Attribute Reduction

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Transactions on Rough Sets IX

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 5390))

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Abstract

In the paper, some generalizations of the notions of reduct, test (superreduct), partial (approximate) reduct and partial test are considered. The accuracy of greedy algorithm for construction of partial test is investigated. A lower bound on the minimal cardinality of partial reducts based on an information about greedy algorithm work is studied. A bound on the precision of greedy algorithm which does not depend on the number of pairs of rows of a decision table which should be separated is obtained. Results of experiments with greedy algorithm are discussed.

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References

  1. Feige, U.: A threshold of ln n for approximating set cover (Preliminary version). In: Proceedings of 28th Annual ACM Symposium on the Theory of Computing, pp. 314–318 (1996)

    Google Scholar 

  2. Grzymala-Busse, J.W.: Data with missing attribute values: Generalization of indiscernibility relation and rule induction. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B.z., Świniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 78–95. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  3. Johnson, D.S.: Approximation algorithms for combinatorial problems. J. Comput. System Sci. 9, 256–278 (1974)

    Article  MATH  Google Scholar 

  4. Kryszkiewicz, M.: Rules in incomplete information systems. Information Sciences 113, 271–292 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  5. Lovász, L.: On the ratio of optimal integral and fractional covers. Discrete Math. 13, 383–390 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  6. Moshkov, M.J., Piliszczuk, M., Zielosko, B.: On construction of partial reducts and irreducible partial decision rules. Fundamenta Informaticae 75(1-4), 357–374 (2007)

    MathSciNet  MATH  Google Scholar 

  7. Moshkov, M.J., Piliszczuk, M., Zielosko, B.: On partial covers, reducts and decision rules with weights. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J.W., Orłowska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI. LNCS, vol. 4374, pp. 211–246. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Moshkov, M.J., Piliszczuk, M., Zielosko, B.: Universal attribute reduction problem. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds.) RSEISP 2007. LNCS, vol. 4585, pp. 417–426. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  9. Moshkov, M.J., Piliszczuk, M., Zielosko, B.: On partial covers, reducts and decision rules. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets VIII. LNCS, vol. 5084, pp. 258–296. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  10. Newman, D.J., Hettich, S., Blake, C.L., Merz, C.J.: UCI Repository of machine learning databases. University of California, Irvine, Department of Information and Computer Sciences (1998), http://www.ics.uci.edu/~mlearn/MLRepository.html

  11. Nguyen, H.S.: Approximate Boolean reasoning: foundations and applications in data mining. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets V. LNCS, vol. 4100, pp. 344–523. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Nguyen, H.S., Ślȩzak, D.: Approximate reducts and association rules - correspondence and complexity results. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS, vol. 1711, pp. 137–145. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  13. Nigmatullin, R.G.: Method of steepest descent in problems on cover. In: Memoirs of Symposium Problems of Precision and Efficiency of Computing Algorithms, Kiev, USSR, vol. 5, pp. 116–126 (1969) (in Russian)

    Google Scholar 

  14. Pawlak, Z.: Rough Sets – Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)

    MATH  Google Scholar 

  15. Pawlak, Z.: Rough set elements. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 1. Methodology and Applications (Studies in Fuzziness and Soft Computing 18), pp. 10–30. Phisica-Verlag, Springer-Verlag (1998)

    Google Scholar 

  16. Pawlak, Z., Skowron, A.: Rudiments of rough sets. Information Sciences 177(1), 3–27 (2007); Rough sets: Some extensions. Information Sciences 177(1), 28–40 (2007); Rough sets and boolean reasoning. Information Sciences 177(1), 41–73 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Piliszczuk, M.: On greedy algorithm for partial reduct construction. In: Proceedings of Concurrency, Specification and Programming Workshop, Ruciane-Nida, Poland, vol. 2, pp. 400–411 (2005)

    Google Scholar 

  18. Quafafou, M.: α-RST: a generalization of rough set theory. Information Sciences 124, 301–316 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  19. Raz, R., Safra, S.: A sub-constant error-probability low-degree test, and sub-constant error-probability PCP characterization of NP. In: Proceedings of 29th Annual ACM Symposium on the Theory of Computing, pp. 475–484 (1997)

    Google Scholar 

  20. Skowron, A.: Rough sets in KDD. In: Proceedings of the 16th World Computer Congress (IFIP 2000), Beijing, China, pp. 1–14 (2000)

    Google Scholar 

  21. Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems. In: Slowinski, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Set Theory, pp. 331–362. Kluwer Academic Publishers, Dordrecht (1992)

    Google Scholar 

  22. Slavík, P.: A tight analysis of the greedy algorithm for set cover (extended abstract). In: Proceedings of 28th Annual ACM Symposium on the Theory of Computing, pp. 435–441 (1996)

    Google Scholar 

  23. Slavík, P.: Approximation algorithms for set cover and related problems. Ph.D. thesis. University of New York, Buffalo (1998)

    Google Scholar 

  24. Ślȩzak, D.: Approximate reducts in decision tables. In: Proceedings of the Congress Information Processing and Management of Uncertainty in Knowledge-based Systems, Granada, Spain, vol. 3, pp. 1159–1164 (1996)

    Google Scholar 

  25. Ślȩzak, D.: Normalized decision functions and measures for inconsistent decision tables analysis. Fundamenta Informaticae 44, 291–319 (2000)

    MathSciNet  Google Scholar 

  26. 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, Heidelberg (2000)

    Google Scholar 

  27. Ślȩzak, D.: Approximate decision reducts. Ph.D. thesis. Warsaw University (2001) (in Polish)

    Google Scholar 

  28. Ślȩzak, D.: Approximate entropy reducts. Fundamenta Informaticae 53, 365–390 (2002)

    MathSciNet  Google Scholar 

  29. Wróblewski, J.: Ensembles of classifiers based on approximate reducts. Fundamenta Informaticae 47, 351–360 (2001)

    MathSciNet  MATH  Google Scholar 

  30. Yablonskii, S.V.: Tests. In: Glushkov, V.M. (ed.) Encyclopedia of Cybernetics (in Russian), pp. 431–432. Main Editorial Board of Ukrainian Soviet Encyclopedia, Kiev (1975)

    Google Scholar 

  31. Ziarko, W.: Analysis of uncertain information in the framework of variable precision rough sets. Foundations of Computing and Decision Sciences 18, 381–396 (1993)

    MATH  Google Scholar 

  32. Zielosko, B.: On partial decision rules. In: Proceedings of Concurrency, Specification and Programming Workshop, Ruciane-Nida, Poland, vol. 2, pp. 598–609 (2005)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Silesia, 39, Bȩdzińska St., Sosnowiec, 41-200, Poland

    Mikhail Ju. Moshkov & Beata Zielosko

  2. ING Bank Śla̧ski S.A., 34, Sokolska St., Katowice, 40-086, Poland

    Marcin Piliszczuk

Authors
  1. Mikhail Ju. Moshkov
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  2. Marcin Piliszczuk
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  3. Beata Zielosko
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  3. Institute of Computer Science, Warsaw University of Technology, Nowowoiejska 15/19, 00-665, Warsaw, Poland

    Henryk Rybiński

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Moshkov, M.J., Piliszczuk, M., Zielosko, B. (2008). Universal Problem of Attribute Reduction. In: Peters, J.F., Skowron, A., Rybiński, H. (eds) Transactions on Rough Sets IX. Lecture Notes in Computer Science, vol 5390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89876-4_11

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  • DOI: https://doi.org/10.1007/978-3-540-89876-4_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89875-7

  • Online ISBN: 978-3-540-89876-4

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