Evolutionary Fuzzy Rules for Ordinal Binary Classification with Monotonicity Constraints

Abstract

We present an approach to learn fuzzy binary decision rules from ordinal temporal data where the task is to classify every instance at each point in time. We assume that one class is preferred to the other, e.g. the undesirable class must not be misclassified. Hence it is appealing to use the Variable Consistency Dominance-based Rough Set Approach (VC-DRSA) to exploit preference information about the problem. In this framework, the VC-DomLEM algorithm has been used to generate the minimal set of consistent rules. Every attribute is then fuzzified by first applying a crisp clustering to the rules’ antecedent thresholds and second using the cluster centroids as indicator for the overlap of neighboring trapezoidal normal membership functions. The widths of the neighboring fuzzy sets are finally tuned by an evolutionary algorithm trying to minimize the specificity of the current fuzzy rule base.

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References

  1. Błaszczyński, J., Słowiński, R., Szeląg, M.: Sequential covering rule induction algorithm for variable consistency rough set approaches. Information Sciences 181(5), 987–1002 (2011), doi:10.1016/j.ins.2010.10.030MathSciNetCrossRefGoogle Scholar
  2. Greco, S., Matarazzo, B., Słowiński, R., Stefanowski, J.: Variable Consistency Model of Dominance-Based Rough Sets Approach. In: Ziarko, W., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 170–181. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. Greco, S., Matarazzo, B., Słowiński, R.: Dominance-based rough set approach to decision under uncertainty and time preference. Annals of Operations Research 176(1), 41–75 (2010), doi:10.1007/s10479-009-0566-8MathSciNetMATHCrossRefGoogle Scholar
  4. Ishibuchi, H., Nakashima, T., Murata, T.: Three-objective genetics-based machine learning for linguistic rule extraction. Information Sciences 136(1-4), 109–133 (2001), doi:10.1016/S0020-0255(01)00144-XMATHCrossRefGoogle Scholar
  5. MacQueen, J.: Some methods for classification and analysis of multivariate observations. In: Cam, L.M.L., Neyman, J. (eds.) Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297. University of California Press, Berkeley (1967)Google Scholar
  6. Moewes, C.: Application of support vector machines to discriminate vehicle crash events. Diploma thesis, School of Computer Science, University of Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany (2007)Google Scholar
  7. Moewes, C., Kruse, R.: Unification of fuzzy SVMs and rule extraction methods through imprecise domain knowledge. In: Verdegay, J.L., Magdalena, L., Ojeda-Aciego, M. (eds.) Proceedings of the International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2008), Torremolinos (Málaga), pp. 1527–1534 (2008)Google Scholar
  8. Moewes, C., Kruse, R.: Zuordnen von linguistischen Ausdrücken zu Motiven in Zeitreihen (Matching of Labeled Terms to Time Series Motifs). Automatisierungstechnik 57(3), 146–154 (2009), doi:10.1524/auto.2009.0760CrossRefGoogle Scholar
  9. Moewes, C., Kruse, R.: On the usefulness of fuzzy SVMs and the extraction of fuzzy rules from SVMs. In: Galichet, S., Montero, J., Mauris, G. (eds.) Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2011) and LFA-2011, Advances in Intelligent Systems Research, vol. 17, pp. 943–948. Atlantis Press, Amsterdam (2011), doi:10.2991/eusflat.2011.46 Google Scholar
  10. Moewes, C., Otte, C., Kruse, R.: Tackling Multiple-Instance Problems in Safety-Related Domains by Quasilinear SVM. In: Dubois, D., Lubiano, M.A., Prade, H., Ángeles Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds.) Soft Methods for Handling Variability and Imprecision. AISC, vol. 48, pp. 409–416. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  11. Moewes, C., Otte, C., Kruse, R.: Simple machine learning approaches to safety-related systems. In: De, R.K., Mandal, D.P., Ghosh, A. (eds.) Machine Interpretation of Patterns: Image Analysis and Data Mining. Statistical Science and Interdisciplinary Research, vol. 11, pp. 231–249. World Scientific Publishing Co. Inc., Hackensack (2010)CrossRefGoogle Scholar
  12. Nauck, D., Kruse, R.: A neuro-fuzzy method to learn fuzzy classification rules from data. Fuzzy Sets and Systems 89(3), 277–288 (1997), doi:10.1016/S0165-0114(97)00009-2MathSciNetCrossRefGoogle Scholar
  13. Nusser, S.: Robust learning in safety-related domains: Machine learning methods for solving safety-related application problems. PhD thesis, School of Computer Science, University of Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany (2009)Google Scholar
  14. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Norwell (1991)MATHGoogle Scholar
  15. Schröder, M., Petersen, R., Klawonn, F., Kruse, R.: Two paradigms of automotive fuzzy logic applications. In: Jamshidi, M., Titli, A., Zadeh, L., Boverie, S. (eds.) Applications of Fuzzy Logic: Towards High Machine Intelligence Quotient Systems. Environmental and Intelligent Manufacturing Systems Series, vol. 9, pp. 153–174. Prentice-Hall, Inc., Upper Saddle River (1997)Google Scholar
  16. Wang, J., Lee, C.: Self-adaptive neuro-fuzzy inference systems for classification applications. IEEE Transactions on Fuzzy Systems 10(6), 790–802 (2002), doi:10.1109/TFUZZ.2002.805880CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Faculty of Computer ScienceOtto-von-Guericke University of MagdeburgMagdeburgGermany

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