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From Vagueness to Rough Sets in Partial Approximation Spaces

  • Zoltán Ernő Csajbók
  • Tamás Mihálydeák
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8537)

Abstract

Vagueness has a central role in the motivation basis of rough set theory. Expressing vagueness, after Frege, Pawlak’s information-based proposal was the boundary regions of sets. In rough set theory, Pawlak represented boundaries by the differences of upper and lower approximations and defined exactness and roughness of sets via these differences. However, defining exactness/roughness of sets have some possibilities in general. In this paper, categories of vagueness, i.e., different kinds of rough sets, are identified in partial approximation spaces. Their formal definitions and intuitive meanings are given under sensible restrictions.

Keywords

Vagueness partial approximation spaces categories of rough sets 

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References

  1. 1.
    Banerjee, M., Chakraborty, M.: Algebras from rough sets. In: Pal, S., Polkowski, L., Skowron, A. (eds.) Rough-Neuro Computing: Techniques for Computing with Words, pp. 157–184. Springer, Berlin (2004)CrossRefGoogle Scholar
  2. 2.
    Ciucci, D.: Approximation algebra and framework. Fundamenta Informaticae 94, 147–161 (2009)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Csajbók, Z., Mihálydeák, T.: Partial approximative set theory: A generalization of the rough set theory. International Journal of Computer Information Systems and Industrial Management Applications 4, 437–444 (2012)zbMATHGoogle Scholar
  4. 4.
    Csajbók, Z., Mihálydeák, T.: A general set theoretic approximation framework. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) IPMU 2012, Part I. CCIS, vol. 297, pp. 604–612. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  5. 5.
    Csajbók, Z.E.: Approximation of sets based on partial covering. In: Peters, J.F., Skowron, A., Ramanna, S., Suraj, Z., Wang, X. (eds.) Transactions on Rough Sets XVI. LNCS, vol. 7736, pp. 144–220. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  6. 6.
    Csajbók, Z.E., Mihálydeák, T.: Fuzziness in partial approximation framework. In: Ganzha, M., Maciaszek, L.A., Paprzycki, M. (eds.) Proceedings of the 2013 Federated Conference on Computer Science and Information Systems, Kraków, Poland (FedCSIS 2013), September 8-11. Annals of Computer Science and Information Systems, Polish Information Processing Society, vol. 1, pp. 35–41. Polskie Towarzystwo Informatyczne (PTI), IEEE Computer Society Press, Warsaw, Poland (2013)Google Scholar
  7. 7.
    Järvinen, J.: Lattice theory for rough sets. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J.W., Orłowska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI. LNCS, vol. 4374, pp. 400–498. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets: A tutorial. In: Pal, S., Skowron, A. (eds.) Rough Fuzzy Hybridization. A New Trend in Decision-Making, pp. 3–98. Springer, Singapore (1999)Google Scholar
  9. 9.
    Pagliani, P.: A pure logic-algebraic analysis of rough top and rough bottom equalities. In: Ziarko, W. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, Proceedings of the International Workshop on Rough Sets and Knowledge Discovery (RSKD 1993), Banff, Alberta, Canada, October 12-15. Workshops in Computing, pp. 225–236. Springer (1993)Google Scholar
  10. 10.
    Pagliani, P., Chakraborty, M.: A Geometry of Approximation: Rough Set Theory Logic, Algebra and Topology of Conceptual Patterns (Trends in Logic). Springer Publishing Company, Incorporated (2008)Google Scholar
  11. 11.
    Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11(5), 341–356 (1982)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)CrossRefGoogle Scholar
  13. 13.
    Yao, Y.Y.: Granular computing using neighborhood systems. In: Roy, R., Furuhashi, T., Chawdhry, P.K. (eds.) Advances in Soft Computing: Engineering Design and Manufacturing. The 3rd On-line World Conference on Soft Computing (WSC3), pp. 539–553. Springer, London (1999)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Zoltán Ernő Csajbók
    • 1
  • Tamás Mihálydeák
    • 2
  1. 1.Department of Health Informatics, Faculty of HealthUniversity of DebrecenNyíregyházaHungary
  2. 2.Department of Computer Science, Faculty of InformaticsUniversity of DebrecenDebrecenHungary

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