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Approximation Spaces in Multi Relational Knowledge Discovery

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Transactions on Rough Sets VI

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 4374))

Abstract

Pawlak introduced approximation spaces in his seminal work on rough sets more than two decades ago. In this paper, we show that approximation spaces are basic structures for knowledge discovery from multi-relational data. The utility of approximation spaces as fundamental objects constructed for concept approximation is emphasized. Examples of basic concepts are given throughout this paper to illustrate how approximation spaces can be beneficially used in many settings. The contribution of this paper is the presentation of an approximation space-based framework for doing research in various forms of knowledge discovery in multi relational data.

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References

  1. Bonchi, F., Boulicaut, J.-F. (eds.): Knowledge Discovery in Inductive Databases. LNCS, vol. 3933. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  2. Dzeroski, S., Lavrac, N. (eds.): Relational Data Mining. Springer, Berlin (2001)

    MATH  Google Scholar 

  3. Łukasiewicz, J.: Die logischen Grundlagen der Wahrscheinlichkeitsrechnung, Kraków 1913. In: Borkowski, L. (ed.) Jan Łukasiewicz - Selected Works, North-Holland, Amsterdam (1970)

    Google Scholar 

  4. Milton, R.S., Maheswari, V.U., Siromoney, A.: Rough Sets and Relational Learning. In: Peters, J.F., et al. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 321–337. Springer, Heidelberg (2004)

    Google Scholar 

  5. Orłowska, E., Szałas, A. (eds.): Relational Methods for Computer Science Applications. Physica–Verlag, Heidelberg (2001)

    Google Scholar 

  6. Pal, S.K., Polkowski, L., Skowron, A. (eds.): Rough-Neural Computing: Techniques for Computing with Words. Springer, Berlin (2004)

    MATH  Google Scholar 

  7. Pawlak, Z.: Rough sets. International J. Comp. Inform. Science 11, 341–356 (1982)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  9. Polkowski, L., Skowron, A. (eds.): Rough Sets in Knowledge Discovery 1 and 2. Physica-Verlag, Heidelberg (1998)

    Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  11. Skowron, A., et al.: Calculi of Approximation Spaces. Fundamenta Informaticae 72(1–3), 363–378 (2006)

    MATH  MathSciNet  Google Scholar 

  12. Stepaniuk, J.: Rough relations and logics. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 1. Methodology and Applications, pp. 248–260. Physica Verlag, Heidelberg (1998)

    Google Scholar 

  13. Stepaniuk, J.: Knowledge Discovery by Application of Rough Set Models. In: Polkowski, L., Tsumoto, S., Lin, T.Y. (eds.) Rough Set Methods and Applications. New Developments in Knowledge Discovery in Information Systems, pp. 137–233. Physica–Verlag, Heidelberg (2000)

    Google Scholar 

  14. Stepaniuk, J., Góralczuk, L.: An Algorithm Generating First Order Rules Based on Rough Set Methods (in Polish). In: Stepaniuk, J. (ed.) Zeszyty Naukowe Politechniki Białostockiej Informatyka nr. 1, pp. 235–250 (2002)

    Google Scholar 

  15. Stepaniuk, J., Honko, P.: Learning First–Order Rules: A Rough Set Approach. Fundamenta Informaticae 61(2), 139–157 (2004)

    MATH  MathSciNet  Google Scholar 

  16. Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46, 39–59 (1993)

    Article  MATH  MathSciNet  Google Scholar 

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James F. Peters Andrzej Skowron Ivo Düntsch Jerzy Grzymała-Busse Ewa Orłowska Lech Polkowski

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Stepaniuk, J. (2007). Approximation Spaces in Multi Relational Knowledge Discovery. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J., Orłowska, E., Polkowski, L. (eds) Transactions on Rough Sets VI. Lecture Notes in Computer Science, vol 4374. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71200-8_19

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  • DOI: https://doi.org/10.1007/978-3-540-71200-8_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71198-8

  • Online ISBN: 978-3-540-71200-8

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