Skip to main content
SpringerLink
Log in

An Introduction to Rough Sets

  • Chapter
Rough Sets: Selected Methods and Applications in Management and Engineering

Part of the book series: Advanced Information and Knowledge Processing ((AI&KP))

Abstract

Fundamental philosophy, concepts and notions of rough set theory (RST) are reviewed. Emphasis is on a constructive formulation and interpretation of rough set approximations. We restrict our discussions to classical RST introduced by Pawlak, with some brief references to the existing extensions. Whenever possible, we provide multiple equivalent definitions of fundamental RST notions in order to better illustrate their usefulness. We also refer to principles of RST based data analysis that can be used to mine data gathered in information tables.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Notes

  1. 1.

    http://lightning.eecs.ku.edu/LERS.html.

  2. 2.

    http://www.lcb.uu.se/tools/rosetta/.

  3. 3.

    http://logic.mimuw.edu.pl/~rses/.

  4. 4.

    http://rseslib.mimuw.edu.pl/.

  5. 5.

    http://www.mimuw.edu.pl/~bazan/roughice/?sLang=en.

References

  1. Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  3. Pawlak, Z., Skowron, A.: Rudiments of rough sets. Inf. Sci. 177(1), 3–27 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Pawlak, Z., Skowron, A.: Rough sets: some extensions. Inf. Sci. 177(1), 28–40 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Crespo, F., Peters, G., Weber, R.: Rough clustering approaches for dynamic environments. In: Peters, G., et al. (eds.) Rough Sets: Selected Methods and Applications in Management and Engineering. Springer, Berlin (2012)

    Google Scholar 

  6. Lingras, P., Butz, C., Bhalchandra, P.: Financial series forecasting using dual rough support vector regression. In: Peters, G., et al. (eds.) Rough Sets: Selected Methods and Applications in Management and Engineering. Springer, Berlin (2012)

    Google Scholar 

  7. Hunter, M.G., Peters, G.: Grounding information technology project critical success factors within the organization: applying rough sets. In: Peters, G., et al. (eds.) Rough Sets: Selected Methods and Applications in Management and Engineering. Springer, Berlin (2012)

    Google Scholar 

  8. Peters, G., Tagg, R.: Workflow management supported by rough set concepts. In: Peters, G., et al. (eds.) Rough Sets: Selected Methods and Applications in Management and Engineering. Springer, Berlin (2012)

    Google Scholar 

  9. Sikora, M., Sikora, B.: Rough natural hazards monitoring. In: Peters, G., et al. (eds.) Rough Sets: Selected Methods and Applications in Management and Engineering. Springer, Berlin (2012)

    Google Scholar 

  10. Ramanna, S., Peters, J.F.: Nearness of associated rough sets. In: Peters, G., et al. (eds.) Rough Sets: Selected Methods and Applications in Management and Engineering. Springer, Berlin (2012)

    Google Scholar 

  11. Słowiński, R. (ed.): Intelligent Decision Support, Handbook of Applications and Advances of the Rough Sets Theory. Kluwer Academic, Dordrecht (1992)

    MATH  Google Scholar 

  12. Lin, T.Y., Lin, T.Y., Cercone, N. (eds.): Rough Sets and Data Mining: Analysis for Imprecise Data. Springer, Berlin (1997)

    Google Scholar 

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

    Google Scholar 

  14. Hassanien, A.E., Suraj, Z., Ślęzak, D., Lingras, P. (eds.): Rough Computing: Theories, Technologies and Applications. IGI Global, Hershey (2007)

    Google Scholar 

  15. Bazan, J.: Hierarchical classifiers for complex spatio-temporal concepts. LNCS Trans. Rough Sets IX, LNCS 5390, 474–750 (2008)

    Article  Google Scholar 

  16. Grzymała-Busse, J.W., Ziarko, W.: Rough sets and data mining. In: Wang, J. (ed.) Encyclopedia of Data Warehousing and Mining, 2nd edn., pp. 1696–1701. IGI Global, Hershey (2009)

    Google Scholar 

  17. Yao, Y.Y.: Interpreting concept learning in cognitive informatics and granular computing. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 39, 855–866 (2009)

    Article  Google Scholar 

  18. Skowron, A., Stepaniuk, J., Świniarski, R.: Modeling rough granular computing based on approximation spaces. Inf. Sci. 184, 20–43 (2012)

    Article  Google Scholar 

  19. Pawlak, Z.: Information systems, theoretical foundations. Inf. Syst. 6(3), 205–218 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  20. Kryszkiewicz, M.: Rough set approach to incomplete information systems. Inf. Sci. 112, 39–49 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  21. Guan, Y.Y., Wang, H.K.: Set-valued information systems. Inf. Sci. 176, 2507–2525 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  22. Lipski, W. Jr.: On semantic issues connected with incomplete information databases. ACM Trans. Database Syst. 4, 269–296 (1979)

    Article  Google Scholar 

  23. Van Mechelen, I., Hampton, J., Michalski, R.S., Theuns, P. (eds.): Categories and Concepts, Theoretical Views and Inductive Data Analysis. Academic Press, San Diego (1993)

    Google Scholar 

  24. Orłowska, E.: Logical aspects of learning concepts. Int. J. Approx. Reason. 2, 349–364 (1988)

    Article  MATH  Google Scholar 

  25. Mitchell, T.: Machine Learning. McGraw Hill, New York (1997)

    MATH  Google Scholar 

  26. Nguyen, H.S.: Approximate Boolean reasoning: foundations and applications in data mining. LNCS Trans. Rough Sets V, LNCS 4100, 334–506 (2006)

    Article  Google Scholar 

  27. Greco, S., Matarazzo, B., Słowiński, R.: Dominance-based rough set approach to decision under uncertainty and time preference. Ann. Oper. Res. 176(1), 41–75 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  28. Wu, W.Z., Zhang, W.X., Li, H.Z.: Knowledge acquisition in incomplete fuzzy information systems via the rough set approach. Expert Syst. 20, 280–286 (2003)

    Article  Google Scholar 

  29. Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundam. Inform. 27(2–3), 245–253 (1996)

    MathSciNet  MATH  Google Scholar 

  30. Jensen, R., Shen, Q.: Computational Intelligence and Feature Selection: Rough and Fuzzy Approaches. Wiley, Hoboken (2008)

    Book  Google Scholar 

  31. Bazan, J.G., Szczuka, M.S.: The rough set exploration system. LNCS Trans. Rough Sets III, LNCS 3400, 37–56 (2005)

    Article  Google Scholar 

  32. Lingras, P., Peters, G.: Applying rough set concepts to clustering. In: Peters, G., et al. (eds.) Rough Sets: Selected Methods and Applications in Management and Engineering. Springer, Berlin (2012)

    Google Scholar 

  33. Ślęzak, D., Wróblewski, J., Eastwood, V., Synak, P.: Brighthouse: an analytic data warehouse for ad-hoc queries. Proc. VLDB Endow. 1, 1337–1345 (2008)

    Google Scholar 

  34. Yao, Y.Y.: A note on definability and approximations. LNCS Trans. Rough Sets VII, LNCS 4400, 274–282 (2007)

    Article  Google Scholar 

  35. Grzymała-Busse, J.W.: LERS—a data mining system. In: Maimon, O., Rokach, L. (eds.) The Data Mining and Knowledge Discovery Handbook, pp. 1347–1351. Springer, Berlin (2005)

    Chapter  Google Scholar 

  36. Yao, Y.Y.: Two views of the theory of rough sets in finite universes. Int. J. Approx. Reason. 15(4), 291–317 (1996)

    Article  MATH  Google Scholar 

  37. Yao, Y.Y.: Three-way decisions using rough sets. In: Peters, G., et al. (eds.) Rough Sets: Selected Methods and Applications in Management and Engineering. Springer, Berlin (2012)

    Google Scholar 

  38. Ziarko, W.: Variable precision rough set model. J. Comput. Syst. Sci. 46(1), 39–59 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  39. Yao, Y.Y.: Probabilistic rough set approximations. Int. J. Approx. Reason. 49, 255–271 (2008)

    Article  MATH  Google Scholar 

  40. Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 17, 191–209 (1990)

    Article  MATH  Google Scholar 

  41. Widz, S., Ślęzak, D.: Rough set based decision support—models easy to interpret. In: Peters, G., et al. (eds.) Rough Sets: Selected Methods and Applications in Management and Engineering. Springer, Berlin (2012)

    Google Scholar 

  42. Mrózek, A.: Rough sets and dependency analysis among attributes in computer implementations of expert’s inference models. Int. J. Man-Mach. Stud. 30(4), 457–473 (1989)

    Article  MATH  Google Scholar 

  43. Suraj, Z.: Rough set method for synthesis and analysis of concurrent processes. In: Polkowski, L., et al. (eds.) New Developments in Knowledge Discovery in Information Systems, pp. 379–490. Physica-Verlag, Heidelberg (2000)

    Google Scholar 

  44. Geng, L., Hamilton, H.J.: Interestingness measures for data mining: a survey. ACM Comput. Surv. 38(3) (2006)

    Google Scholar 

  45. Guyon, I., Aliferis, C., Elisseeff, A.: Causal feature selection. In: Liu, H., Motoda, H. (eds.) Computational Methods of Feature Selection, pp. 63–86. Chapman & Hall/CRC, Boca Raton (2008)

    Google Scholar 

  46. Qian, Y., Liang, J., Pedrycz, W., Dang, C.: Positive approximation: an accelerator for attribute reduction in rough set theory. Artif. Intell. 174(9–10), 597–618 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  47. Banka, H., Mitra, S.: Feature selection, classification and rule generation using rough sets. In: Peters, G., et al. (eds.) Rough Sets: Selected Methods and Applications in Management and Engineering. Springer, Berlin (2012)

    Google Scholar 

  48. Ślęzak, D.: Rough sets and functional dependencies in data: foundations of association reducts. LNCS Trans. Comput. Sci. V, LNCS 5540, 182–205 (2009)

    Article  Google Scholar 

  49. Düntsch, I., Gediga, G.: Uncertainty measures of rough set prediction. Artif. Intell. 106(1), 109–137 (1998)

    Article  MATH  Google Scholar 

  50. Ślęzak, D.: Various approaches to reasoning with frequency based decision reducts: a survey. In: Polkowski, L., et al. (eds.) New Developments in Knowledge Discovery in Information Systems, pp. 235–288. Physica-Verlag, Heidelberg (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Yiyu Yao

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

    Dominik Ślęzak

  3. Infobright Inc., Poland, Krzywickiego 34 pok. 219, 02-078, Warsaw, Poland

    Dominik Ślęzak

Authors
  1. Yiyu Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dominik Ślęzak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yiyu Yao .

Editor information

Editors and Affiliations

  1. Munich University of Applied Sciences, Lothstrasse 34, Munich, 80335, Germany

    Georg Peters

  2. Dpt. of Mathematics and Computer Science, St. Mary's University, Halifax, B3H 3C3, Nova Scotia, Canada

    Pawan Lingras

  3. University of Warsaw, Banacha 2, Warsaw, 02-097, Poland

    Dominik Ślęzak

  4. Department of Computer Science, University of Regina, Regina, S4S0A2, Saskatchewan, Canada

    Yiyu Yao

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag London Limited

About this chapter

Cite this chapter

Yao, Y., Ślęzak, D. (2012). An Introduction to Rough Sets. In: Peters, G., Lingras, P., Ślęzak, D., Yao, Y. (eds) Rough Sets: Selected Methods and Applications in Management and Engineering. Advanced Information and Knowledge Processing. Springer, London. https://doi.org/10.1007/978-1-4471-2760-4_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-2760-4_1

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2759-8

  • Online ISBN: 978-1-4471-2760-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation