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On Different Ways of Handling Inconsistencies in Ordinal Classification with Monotonicity Constraints

  • Jerzy Błaszczyński
  • Weibin Deng
  • Feng Hu
  • Roman Słowiński
  • Marcin Szeląg
  • Guoyin Wang
Part of the Communications in Computer and Information Science book series (CCIS, volume 297)

Abstract

Ordinal classification problem with monotonicity constraints involves a monotonic relationship between the description of an object and the class to which it is assigned. An example of such a relationship is: “the higher the quality of service and the lower the price, the higher the customer satisfaction level (class)”. Violation of the monotonic relationship is considered as an inconsistency. Rough set approaches to induction of the monotonic relationships in form of decision rules handle these inconsistencies at the stage of data pre-processing. As a result, the data sufficiently consistent for rule induction are identified. In this paper, we compare two ways of handling inconsistencies. The first one consists in distinguishing objects that are not less consistent than a specified threshold from those which are less consistent. The second one involves iterative removal of the most inconsistent objects until the data set is consistent. We present results of a computational experiment, in which rule classifiers are induced from data pre-processed in the two considered ways.

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References

  1. 1.
    Ben-David, A.: Monotonicity maintenance in information-theoretic machine learning algorithms. Machine Learning 19(1), 29–43 (1995)Google Scholar
  2. 2.
    Ben-David, A., Sterling, L., Tran, T.: Adding monotonicity to learning algorithms impair their accuracy. Expert Systems with Applications 36(3), 6627–6634 (2009)CrossRefGoogle Scholar
  3. 3.
    Błaszczyński, J., Greco, S., Słowiński, R.: Multi-criteria classification – a new scheme for application of dominance-based decision rules. European Journal of Operational Research 181(3), 1030–1044 (2007)zbMATHCrossRefGoogle Scholar
  4. 4.
    Błaszczyński, J., Greco, S., Słowiński, R., Szeląg, M.: Monotonic variable consistency rough set approaches. International Journal of Approximate Reasoning 50(7), 979–999 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Błaszczyński, J., Słowiński, R., Szeląg, M.: Learnability in Rough Set Approaches. In: Szczuka, M., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds.) RSCTC 2010. LNCS, vol. 6086, pp. 402–411. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Błaszczyński, J., Słowiński, R., Szeląg, M.: Probabilistic Rough Set Approaches to Ordinal Classification with Monotonicity Constraints. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS, vol. 6178, pp. 99–108. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Błaszczyński, J., Słowiński, R., Szeląg, M.: Sequential covering rule induction algorithm for variable consistency rough set approaches. Information Sciences 181, 987–1002 (2011)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Daniels, H., Kamp, B.: Applications of mlp networks to bond rating and house pricing. Neural Computation and Applications 8, 226–234 (1999)CrossRefGoogle Scholar
  9. 9.
    Deng, W., Wang, G., Hu, F.: An Improved Variable Precision Model of Dominance-Based Rough Set Approach. In: Kuznetsov, S.O., Ślęzak, D., Hepting, D.H., Mirkin, B.G. (eds.) RSFDGrC 2011. LNCS, vol. 6743, pp. 60–67. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. 10.
    Deng, W., Wang, G., Yang, S., Hu, F.: A New Method for Inconsistent Multicriteria Classification. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 600–609. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Greco, S., Matarazzo, B., Słowiński, R.: Rough sets theory for multicriteria decision analysis. European Journal of Operational Research 129(1), 1–47 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Greco, S., Matarazzo, B., Słowiński, R.: Granular computing for reasoning about ordered data: the dominance-based rough set approach. In: Pedrycz, W., Skowron, A., Kreinovich, V. (eds.) Handbook of Granular Computing, ch. 15, John Wiley & Sons, Ltd (2008)Google Scholar
  13. 13.
    Inuiguchi, M., Yoshioka, Y.: Variable-Precision Dominance-Based Rough Set Approach. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 203–212. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Koop, G.: Analysis of Economic Data. John Wiley and Sons (2000)Google Scholar
  15. 15.
    Kotłowski, W., Dembczyński, K., Greco, S., Słowiński, R.: Stochastic dominance-based rough set model for ordinal classification. Information Sciences 178(21), 4019–4037 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Słowiński, R., Greco, S., Matarazzo, B.: Rough set based decision support. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, ch. 16, pp. 475–527. Springer, New York (2005)Google Scholar
  17. 17.
    Słowiński, R., Greco, S., Matarazzo, B.: Rough sets in decision making. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and Systems Science, pp. 7753–7786. Springer, New York (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jerzy Błaszczyński
    • 1
  • Weibin Deng
    • 3
    • 4
  • Feng Hu
    • 3
    • 4
  • Roman Słowiński
    • 1
    • 2
  • Marcin Szeląg
    • 1
  • Guoyin Wang
    • 4
    • 5
  1. 1.Institute of Computing SciencePoznań University of TechnologyPoznańPoland
  2. 2.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  3. 3.School of Information Science and TechnologySouthwest Jiaotong UniversityChengduP.R. China
  4. 4.Institute of Computer Science and TechnologyChongqing University of Posts and TelecommunicationsChongqingP.R. China
  5. 5.Institute of Electronic Information TechnologyChongqing Institute of Green and Intelligent Technology, CASChongqingP.R. China

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