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Approximation Spaces in Extensions of Rough Set Theory

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Rough Sets and Current Trends in Computing (RSCTC 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1424))

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Abstract

In this paper we present a generalization of the approximation space notion. We also present difierent notions of rough relations. We point out the role of searching for proper approximation space.

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References

  1. Duentsch, I.: Rough Sets and Algebras of Relations, in: (ed.) E. Orlowska, Incomplete Information: Rough Set Analysis, Physica-Verlag, 1998, pp. 95–108.

    Google Scholar 

  2. Greco, S., Matarazzo, B., Slowinski, R.: Rough Approximation of a Preference Relation in a Pairwise Comparison Table, (eds.) L. Polkowski, A. Skowron, Rough Sets in Knowledge Discovery Part I and II, Physica-Verlag, 1998.

    Google Scholar 

  3. Krawiec, K., Slowinski, R., Vanderpooten, D.: Learning of Decision Rules from Similarity Based Rough Approximations, (eds.) L. Polkowski, A. Skowron, Rough Sets in Knowledge Discovery, Part I and II, Physica-Verlag, 1998.

    Google Scholar 

  4. Kretowski, M., Stepaniuk, J.: Selection of Objects and Attributes, a Tolerance Rough Set Approach, Proceedings of the Poster Session of Ninth International Symposium on Methodologies for Intelligent Systems, June 10–13, 1996, Zakopane, Poland, pp. 169–180.

    Google Scholar 

  5. Nguyen, S.H., Skowron, A., Synak, P.: Discovery of Data Patterns with Applications to Decomposition and Classification Problems, (eds.) L. Polkowski, A. Skowron, Rough Sets in Knowledge Discovery, Part I and II, Physica-Verlag, 1998.

    Google Scholar 

  6. Pawlak, Z.: Rough Relations, Bulletin of the Polish Academy of Sciences, Technical Sciences vol. 34(9–10), 1986, pp. 587–590.

    MATH  MathSciNet  Google Scholar 

  7. Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, 1991.

    Google Scholar 

  8. Skowron, A., Polkowski, L.: Synthesis of Decision Systems from Data Tables, (eds.) T.Y. Lin, N. Cercone, Rough Sets and Data Mining Analysis of Imprecise Data, Kluwer Academic Publishers, 1997, pp. 259–299.

    Google Scholar 

  9. Skowron, A., Polkowski, L., Komorowski J.: Learning Tolerance Relations by Boolean Descriptors: Automatic Feature Extraction from Data Tables, Proceedings of the Fourth International Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery, November 6–8, 1996, Tokyo, Japan, pp. 11–17.

    Google Scholar 

  10. Skowron, A., Stepaniuk, J.: Towards an Approximation Theory of Discrete Problems, Fundamenta Informaticae 15(2), 1991, pp. 187–208.

    MATH  MathSciNet  Google Scholar 

  11. Skowron, A., Stepaniuk, J.: Approximations of Relations, In: W. Ziarko, ed., Rough Sets, Fuzzy Sets and Knowledge Discovery, Springer Verlag 1994, pp. 161–166.

    Google Scholar 

  12. Skowron, A., Stepaniuk, J.: Generalized Approximation Spaces, Proceedings of the Third International Workshop on Rough Sets and Soft Computing, San Jose, November 10–12, 1994, pp. 156–163.

    Google Scholar 

  13. Skowron A., Stepaniuk, J.: Tolerance Approximation Spaces, Fundamenta Informaticae, 27 (1996) pp. 245–253.

    MATH  MathSciNet  Google Scholar 

  14. Slowinski, R.: Strict and Weak Indiscernibility of Objects Described by Quantitative Attributes with Overlapping Norms, Foundations of Computing and Decision Sciences, Vol. 18, 1993, pp. 361–369.

    MATH  MathSciNet  Google Scholar 

  15. Stepaniuk, J.: Properties and Applications of Rough Relations, ICS WUT Research Report 26/96, 1996 and In: Proceedings of the Fifth International Workshop on Intelligent Information Systems, Deblin, Poland, June 2–5, 1996, pp. 136–141.

    Google Scholar 

  16. Stepaniuk, J., Kretowski, M.: Decision System Based on Tolerance Rough Sets, Proceedings of the Fourth International Workshop on Intelligent Information Systems, Augustow, Poland, June 5–9, 1995, pp. 62–73.

    Google Scholar 

  17. Stepaniuk, J.: Approximation Spaces, Reducts and Representatives, (eds.) L. Polkowski, A. Skowron, Rough Sets in Knowledge Discovery, Part I and II, Physica-Verlag, 1998.

    Google Scholar 

  18. Stepaniuk, J.: Rough Relations and Logics, (eds.) L. Polkowski, A. Skowron, Rough Sets in Knowledge Discovery, Part I and II, Physica-Verlag, 1998.

    Google Scholar 

  19. Yao, Y.Y., Wong, S.K.M., Lin, T.Y.: A Review of Rough Set Models, (eds.) T. Y. Lin, N. Cercone, Rough Sets and Data Mining Analysis of Imprecise Data, Kluwer Academic Publishers, 1997, pp. 47–75.

    Google Scholar 

  20. Vakarelov, D.: Rough Polyadic Modal Logics, Journal of Applied Non-Classical Logics, vol. 1(1), 1991, pp. 9–36.

    MATH  MathSciNet  Google Scholar 

  21. Wilson, D.A., Martinez, T.R.: Improved Heterogeneous Distance Functions, Journal of Artificial Intelligence Research, Vol. 6, 1997, pp. 1–34.

    MATH  MathSciNet  Google Scholar 

  22. Ziarko, W.: Variable Precision Rough Sets Model, Journal of Computer and Systems Sciences, Vol. 46, No. 1, 1993, pp. 39–59.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351, Bialystok, Poland

    Jaroslaw Stepaniuk

Authors
  1. Jaroslaw Stepaniuk
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Editor information

Editors and Affiliations

  1. Institute of Mathematics, Warsaw University of Technology, Pl. Politechniki 1, 00-665, Warszawa, Poland

    Lech Polkowski

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warszawa, Poland

    Andrzej Skowron

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© 1998 Springer-Verlag Berlin Heidelberg

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Stepaniuk, J. (1998). Approximation Spaces in Extensions of Rough Set Theory. In: Polkowski, L., Skowron, A. (eds) Rough Sets and Current Trends in Computing. RSCTC 1998. Lecture Notes in Computer Science(), vol 1424. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69115-4_40

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  • DOI: https://doi.org/10.1007/3-540-69115-4_40

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64655-6

  • Online ISBN: 978-3-540-69115-0

  • eBook Packages: Springer Book Archive

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