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Rough Sets and Decision Algorithms

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Rough Sets and Current Trends in Computing (RSCTC 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2005))

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Abstract

Rough set based data analysis starts from a data table, called an in formation system. The information system contains data about objects of interest characterized in terms of some attributes. Often we distinguish in the information system condition and decision attributes. Such information system is called a decision table. The decision table describes decisions in terms of conditions that must be satisfied in order to carry out the decision specified in the decision table. With every decision table a set of decision rules, called a decision algorithm can be associated. It is shown that every decision algorithm reveals some well known probabilistic properties, in particular it satisfies the Total Probability Theorem and the Bayes’ Theorem. These properties give a new method of drawing conclusions from data, without referring to prior and posterior probabilities, inherently associated with Bayesian reasoning.

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References

  1. Adams, E. W. (1975) The logic of conditionals, an application of probability to deductive logic. D. Reidel Publishing Company, Dordrecht, Boston

    MATH  Google Scholar 

  2. Grzymala-Busse J.(1991) Managing Uncertainty in Expert Systems. Kluwer Academic Publishers, Boston, Dordrecht

    Google Scholar 

  3. Lukasiewicz, J. Die logishen Grundlagen der Wahrscheinilchkeitsrechnung. Krakow, 1913. In: L. Borkowski (ed.), Jan Lukasiewicz-Selected Works, North Holland Publishing Company, Amsterdam, London, Polish Scientific Publishers, Warsaw, 1970

    Google Scholar 

  4. Pawlak, Z. (1991) Rough Sets-Theoretical Aspects of Reasoning about Data; Kluwer Academic Publishers: Boston, Dordrecht

    MATH  Google Scholar 

  5. Pawlak, Z.(1999) Decision rules, Bayes' rule and rough sets. In: N. Zhong, A. Skowron, S. Ohsuga (eds.), Proceedings of 7th International Workshop: New Directions in Rough Sets, Data Mining, and Granular-Soft Computing (RSFDGSC'99), Yamaguchi, Japan, November 1999, Lecture Notes in Artificial Intelligence 1711 Springer-Verlag, Berlin, 1–9

    Google Scholar 

  6. Pawlak, Z. Drawing conclusions from data-the rough set way (to appear)

    Google Scholar 

  7. Pawlak, Z. Combining rough sets and Bayes' rule (to appear)

    Google Scholar 

  8. Pawlak, Z.; Skowron, A. (1994) Rough membership functions. In: R.R. Yaeger, M. Fedrizzi, and J. Kacprzyk (eds.), Advances in the Dempster Shafer Theory of Evidence, John Wiley & Sons, Inc., New York, 251–271

    Google Scholar 

  9. Polkowski, L., Skowron, A. (1998) Proceedings of the First International Conference Rough Sets and Current Trends in Computing (RSCTC'98), Warsaw, Poland, June, Lecture Notes in Artificial Intelligence 1424, Springer-Verlag, Berlin

    Google Scholar 

  10. Polkowski, L., Skowron, A. (1998) Rough Sets in Knowledge Discovery Vol. 1-2, Physica-Verlag, Heidelberg

    Google Scholar 

  11. Polkowski, L., Tsumoto, S., Lin, T.Y. Rough Set Methods and Applications. New Development in Knowledge Discovery in Information Systems, Springer-Verlag (to appear)

    Google Scholar 

  12. Ramoni, M., Sebastiani, P. (1999) Bayasian Methods. In: M. Berthold, D. Hand (eds.), Intelligent Data Analysis, An Introduction, Springer, Berlin

    Google Scholar 

  13. Tsumoto, S.; Kobayashi, S. et al. (1996) (eds.), Proceedings of the Fourth International Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery (RSFD'96). The University of Tokyo, November 6-8

    Google Scholar 

  14. Tsumoto, S.(1998) Modelling medical diagnostic rules based on rough sets. In: L. Polkowski, A. Skowron (eds.), Proceedings of the First International Conference Rough Sets and Current Trends in Computing (RSCTC'98), Warsaw, Poland, June, Lecture Notes in Artificial Intelligence 1424, Springer-Verlag, Berlin, 475–482

    Google Scholar 

  15. Ziarko, W. (1998) Variable precision rough set model. Journal of Computer and Systems Sciences 46, 39-59

    Google Scholar 

  16. Ziarko, W. (1998) Approximation region-based decision tables. In: L. Polkowski, A. Skowron (eds.), Rough Sets in Knowledge Discovery Vol.1-2, Physica-Verlag, Heidelberg, 178–185

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, ul. Bałtycka 5, 44 000, Gliwice, Poland

    Zdzisław Pawlak

Authors
  1. Zdzisław Pawlak
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Regina Regina, S4S 0A2, Saskatchewan, Canada

    Wojciech Ziarko  & Yiyu Yao  & 

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© 2001 Springer-Verlag Berlin Heidelberg

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Pawlak, Z. (2001). Rough Sets and Decision Algorithms. In: Ziarko, W., Yao, Y. (eds) Rough Sets and Current Trends in Computing. RSCTC 2000. Lecture Notes in Computer Science(), vol 2005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45554-X_3

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  • DOI: https://doi.org/10.1007/3-540-45554-X_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43074-2

  • Online ISBN: 978-3-540-45554-7

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