Skip to main content
SpringerLink
Log in

A Definition of Structured Rough Set Approximations

  • Conference paper
Rough Sets and Intelligent Systems Paradigms

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8537))

Abstract

Pawlak lower and upper approximations are unions of equivalence classes. By explicitly expressing individual equivalence classes in the approximations, Bryniarski uses a pair of families of equivalence classes as rough set approximations. Although the latter takes into consideration of structural information of the approximations, it has not received its due attention. The main objective of this paper is to further explore the Bryniarski definition and propose a generalized definition of structured rough set approximations by using a family of conjunctively definable sets. The connections to covering-based rough sets and Grzymala-Busse’s LERS systems are investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bryniarski, E.: A calculus of rough sets of the first order. Bulletin of the Polish Academy of Sciences, Mathematics 37, 71–78 (1989)

    MathSciNet  MATH  Google Scholar 

  2. Buszkowski, W.: Approximation spaces and definability for incomplete information systems. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 115–122. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  3. Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17, 191–209 (1990)

    Article  Google Scholar 

  4. Grzymala-Busse, J.W.: A new version of the rule induction system LERS. Fundamenta Informaticae 31, 27–39 (1997)

    MATH  Google Scholar 

  5. Grzymala-Busse, J.W.: LERS - A system for learning from examples based on rough sets. In: Słowiński, R. (ed.) Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, pp. 3–18. Kluwer Academic Publishers, Dordrecht (1992)

    Chapter  Google Scholar 

  6. Hunt, E.B.: Concept Learning: An Information Processing Problem. John Wiley and Sons Inc., New York (1962)

    Book  Google Scholar 

  7. Marek, W., Pawlak, Z.: Information storage and retrieval systems: Mathematical foundations. Theoretical Computer Science 1, 331–354 (1976)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  9. Pawlak, Z.: Rough classification. International Journal of Man-Machine Studies 20, 469–483 (1984)

    Article  Google Scholar 

  10. Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)

    Article  MathSciNet  Google Scholar 

  11. Restrepo, M., Cornelis, C., Gómez, J.: Duality, conjugacy and adjointness of approximation operators in covering-based rough sets. International Journal of Approximate Reasoning 55, 469–485 (2014)

    Article  MathSciNet  Google Scholar 

  12. van Mechelen, I., Hampton, J., Michalski, R., Thenus, P.: Categories and Concepts: Theoretical Views and Inductive Data Analysis. Academic Press, New York (1993)

    Google Scholar 

  13. Yao, Y.Y.: A note on definability and approximations. In: Peters, J.F., Skowron, A., Marek, V.W., Orłowska, E., Słowiński, R., Ziarko, W.P. (eds.) Transactions on Rough Sets VII. LNCS, vol. 4400, pp. 274–282. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Yao, Y.Y.: A partition model of granular computing. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B., Swiniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 232–253. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  15. Yao, Y.Y., Deng, X.F.: A granular computing paradigm for concept learning. In: Ramanna, S., Jain, L.C., Howlett, R.J. (eds.) Emerging Paradigms in ML. SIST, vol. 13, pp. 307–326. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  16. Yao, Y.Y., Fu, R.: The concept of reducts in Pawlak three-step rough set analysis. In: Peters, J.F., Skowron, A., Ramanna, S., Suraj, Z., Wang, X. (eds.) Transactions on Rough Sets XVI. LNCS, vol. 7736, pp. 53–72. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  17. Yao, Y.Y., Yao, B.X.: Covering based rough set approximations. Information Sciences 200, 91–107 (2012)

    Article  MathSciNet  Google Scholar 

  18. Żakowski, W.F.: Approximations in the space (U, Π). Demonstratio Mathematica 16, 761–769 (1983)

    Article  MathSciNet  Google Scholar 

  19. Zhu, W., Wang, F.Y.: Reduction and axiomization of covering generalized rough sets. Information Sciences 152, 217–230 (2003)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Yiyu Yao & Mengjun Hu

Authors
  1. Yiyu Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mengjun Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Computer Science, Warsaw University of Technology, Nowowiejska 15/19, 00-665, Warsaw, Poland

    Marzena Kryszkiewicz  & Zbigniew W. Raś  & 

  2. Department of Computer Science and Artificial Intelligence, University of Granada, Calle del Periodista Daniel Saucedo Aranda s/n, 18071, Granada, Spain

    Chris Cornelis

  3. DISCo, Università di Milano – Bicocca, Viale Sarca 336 – U14, 20126, Milano, Italy

    Davide Ciucci

  4. Dpt. de Matemáticas, University of Càdiz, Spain

    Jesús Medina-Moreno

  5. School of Computing and Information Systems, University of Tasmania, Japan

    Hiroshi Motoda

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Yao, Y., Hu, M. (2014). A Definition of Structured Rough Set Approximations. In: Kryszkiewicz, M., Cornelis, C., Ciucci, D., Medina-Moreno, J., Motoda, H., Raś, Z.W. (eds) Rough Sets and Intelligent Systems Paradigms. Lecture Notes in Computer Science(), vol 8537. Springer, Cham. https://doi.org/10.1007/978-3-319-08729-0_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08729-0_10

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08728-3

  • Online ISBN: 978-3-319-08729-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation