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Probabilistic Granule Analysis

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5306))

Abstract

We present a semi–parametric approach to evaluate the reliability of rules obtained from a rough set information system by replacing strict determinacy by predicting a random variable which is a mixture of latent probabilities obtained from repeated measurements of the decision variable. It is demonstrated that the algorithm may be successfully used for unsupervised learning.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Düntsch, I., Gediga, G.: Statistical evaluation of rough set dependency analysis. International Journal of Human–Computer Studies 46, 589–604 (1997)

    Article  Google Scholar 

  3. Düntsch, I., Gediga, G.: Uncertainty measures of rough set prediction. Artificial Intelligence 106, 77–107 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  4. Browne, C., Düntsch, I., Gediga, G.: IRIS revisited: A comparison of discriminant and enhanced rough set data analysis. In: Polkowski, L., Skowron, A. (eds.) Rough sets in knowledge discovery, vol. 2, pp. 345–368. Physica–Verlag (1998)

    Google Scholar 

  5. Fisher, R.A.: The use of multiple measurements in taxonomic problems. Ann. Eugen. 7, 179–188 (1936)

    Article  Google Scholar 

  6. Gediga, G., Düntsch, I.: Statistical tools for rule based data analysis. In: Komorowski, J., Düntsch, I., Skowron, A. (eds.) Workshop on Synthesis of Intelligent Agent Systems from Experimental Data, ECAI 1998 (1998)

    Google Scholar 

  7. Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46 (1993)

    Google Scholar 

  8. Pawlak, Z.: Rough sets: Theoretical aspects of reasoning about data. System Theory, Knowledge Engineering and Problem Solving, vol. 9. Kluwer, Dordrecht (1991)

    Book  MATH  Google Scholar 

  9. Gediga, G., Düntsch, I.: Rough approximation quality revisited. Artificial Intelligence 132, 219–234 (2001)

    Article  MATH  Google Scholar 

  10. Pawlak, Z., Skowron, A.: Rough sets: Some extensions. Information Sciences 177, 28–40 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Pawlak, Z.: A rough set view on Bayes’ theorem. International Journal of Intelligent Systems 18, 487 (2003)

    Article  MATH  Google Scholar 

  12. Slezak, D., Ziarko, W.: The investigation of the Bayesian rough set model. International Journal of Approximate Reasoning 40, 81–91 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Akaike, H.: Information theory and an extension of the maximum likelihood principle. In: Petrov, B.N., Cáski, F. (eds.) Second International Symposium on Information Theory, Budapest, Akademiai Kaidó, pp. 267–281 (1973); Reprinted in: Kotz, S., Johnson, N.L. (eds.) Breakthroughs in Statistics, vol. I, pp. 599–624. Springer, New York (1992)

    Google Scholar 

  14. Schwarz, G.: Estimating the dimension of a model. Annals of Statistics 6, 461–464 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  15. Redner, R.A., Walker, H.F.: Mixture densities, maximum likelihood and the EM algorithm. SIAM Review 26, 195–236 (1984)

    Article  MathSciNet  MATH  Google Scholar 

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© 2008 Springer-Verlag Berlin Heidelberg

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Düntsch, I., Gediga, G. (2008). Probabilistic Granule Analysis. In: Chan, CC., Grzymala-Busse, J.W., Ziarko, W.P. (eds) Rough Sets and Current Trends in Computing. RSCTC 2008. Lecture Notes in Computer Science(), vol 5306. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88425-5_23

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  • DOI: https://doi.org/10.1007/978-3-540-88425-5_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88423-1

  • Online ISBN: 978-3-540-88425-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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