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PRE and Variable Precision Models in Rough Set Data Analysis

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Transactions on Rough Sets XIX

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 8988))

Abstract

We present a parameter free and monotonic alternative to the parametric variable precision model of rough set data analysis. The proposed model is based on the well known PRE index \(\lambda \) of Goodman and Kruskal. Using a weighted \(\lambda \) model it is possible to define a two dimensional space based on (Rough) sensitivity and (Rough) specificity, for which the monotonicity of sensitivity in a chain of sets is a nice feature of the model. As specificity is often monotone as well, the results of a rough set analysis can be displayed like a receiver operation curve (ROC) in statistics. Another aspect deals with the precision of the prediction of categories – normally measured by an index \(\alpha \) in classical rough set data analysis. We offer a statistical theory for \(\alpha \) and a modification of \(\alpha \) which fits the needs of our proposed model. Furthermore, we show how expert knowledge can be integrated without losing the monotonic property of the index. Based on a weighted \(\lambda \), we present a polynomial algorithm to determine an approximately optimal set of predicting attributes. Finally, we exhibit a connection to Bayesian analysis. We present several simulation studies for the presented concepts. The current paper is an extended version of [1].

Ordering of authors is alphabetical, and equal authorship is implied

Ivo Düntsch– gratefully acknowledges support by the Natural Sciences and Engineering Research Council of Canada.

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Notes

  1. 1.

    For other views of Bayes’ Theorem and its connection to rough sets see e.g. [18–20].

References

  1. Düntsch, I., Gediga, G.: Weighted \(\lambda \) precision models in rough set data analysis. In: Proceedings of the Federated Conference on Computer Science and Information Systems, pp. 309–316. IEEE, Wrocław, Poland (2012)

    Google Scholar 

  2. Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11, 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ziarko, W.: Variable precision rough set model. J. Comput. Syst. Sci. 46, 39–59 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gediga, G., Düntsch, I.: Rough approximation quality revisited. Artif. Intell. 132, 219–234 (2001)

    Article  MATH  Google Scholar 

  5. Beynon, M.: Reducts within the variable precision rough sets model: a further investigation. Eur. J. Oper. Res. 134, 592–605 (2001)

    Article  MATH  Google Scholar 

  6. Zytkow, J.M.: Granularity refined by knowledge: contingency tables and rough sets as tools of discovery. In: Dasarathy, B. (ed.) Proceedings of SPIE 4057, Data Mining and Knowledge Discovery: Theory, Tools, and Technology II., pp. 82–91 (2000)

    Google Scholar 

  7. Hildebrand, D., Laing, J., Rosenthal, H.: Prediction logic and quasi-independence in empirical evaluation of formal theory. J. Math. Sociol. 3, 197–209 (1974)

    Article  MATH  Google Scholar 

  8. Hildebrand, D., Laing, J., Rosenthal, H.: Prediction Analysis of Cross Classification. Wiley, New York (1977)

    Google Scholar 

  9. Goodman, L.A., Kruskal, W.H.: Measures of association for cross classification. J. Am. Stat. Assoc. 49, 732–764 (1954)

    MATH  Google Scholar 

  10. Holte, R.C.: Very simple classification rules perform well on most commonly used datasets. Mach. Learn. 11, 63–90 (1993)

    Article  MATH  Google Scholar 

  11. Wu, S., Flach, P.A.: Feature selection with labelled and unlabelled data. In: Bohanec, M., Kasek, B., Lavrac, N., Mladenic, D. (eds.) ECML/PKDD 2002 workshop on Integration and Collaboration Aspects of Data Mining, pp. 156–167. University of Helsinki (August, Decision Support and Meta-Learning (2002)

    Google Scholar 

  12. Nevill-Manning, C.G., Holmes, G., Witten, I.H.: The development of Holte’s 1R classifier. In: Proceedings of the 2nd New Zealand Two-Stream International Conference on Artificial Neural Networks and Expert Systems. ANNES 1995, pp. 239–246. IEEE Computer Society, Washington, DC, USA(1995)

    Google Scholar 

  13. Düntsch, I., Gediga, G.: Simple data filtering in rough set systems. Int. J. Approx. Reason. 18(1–2), 93–106 (1998)

    Article  MATH  Google Scholar 

  14. Youden, W.: Index for rating diagnostic tests. Cancer 3, 32–35 (1950)

    Article  Google Scholar 

  15. Böhning, D., Böhning, W., Holling, H.: Revisiting youden’s index as a useful measure of the misclassification error in meta-analysis of diagnostic studies. Stat. Methods Med. Res. 17, 543–554 (2008)

    Article  MathSciNet  Google Scholar 

  16. Oehlert, G.: A note on the Delta method. Am. Stat. 46, 27–29 (1992)

    MathSciNet  Google Scholar 

  17. Chen, C.B., Wang, L.Y.: Rough set based clustering with refinement using Shannon’s entropy theory. Comput. Math. Appl. 52, 1563–1576 (2006)

    Article  MathSciNet  Google Scholar 

  18. Pawlak, Z.: A rough set view on Bayes’ theorem. Int. J. Intell. Syst. 18, 487–498 (2003)

    Article  Google Scholar 

  19. Ślȩzak, D.: Rough sets and Bayes factor. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets III. LNCS, vol. 3400, pp. 202–229. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  20. Yao, Y.: Probabilistic rough set approximations. Int. J. Approx. Reason. 49(2), 255–271 (2008)

    Article  MATH  Google Scholar 

  21. Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets. NATO Advanced Studies Institute, vol. 83, pp. 445–470. Springer, Reidel, Dordrecht (1982)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Brock University, St. Catharines, Ontario, L2S 3A1, Canada

    Ivo Düntsch

  2. Department of Psychology, Institut IV, Universität Münster, Fliednerstr. 21, Münster, Germany

    Günther Gediga

Authors
  1. Ivo Düntsch
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  2. Günther Gediga
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Corresponding author

Correspondence to Ivo Düntsch .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, University of Manitoba, Winnipeg, Manitoba, Canada

    James F. Peters

  2. University of Warsaw, Warsaw, Poland

    Andrzej Skowron

  3. University of Warsaw, Warsaw, Poland

    Dominik Ślȩzak

  4. University of Warsaw, Warsaw, Poland

    Hung Son Nguyen

  5. University of Rzeszów, Rzeszów, Poland

    Jan G. Bazan

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Düntsch, I., Gediga, G. (2015). PRE and Variable Precision Models in Rough Set Data Analysis. In: Peters, J., Skowron, A., Ślȩzak, D., Nguyen, H., Bazan, J. (eds) Transactions on Rough Sets XIX. Lecture Notes in Computer Science(), vol 8988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47815-8_2

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  • DOI: https://doi.org/10.1007/978-3-662-47815-8_2

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  • Print ISBN: 978-3-662-47814-1

  • Online ISBN: 978-3-662-47815-8

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