Skip to main content
SpringerLink
Log in

A Semantical Approach to Rough Sets and Dominance-Based Rough Sets

  • Conference paper
  • First Online:
Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 611))

Abstract

There exist two formulations of rough sets: the conceptual and computational one. The conceptual or semantical approach of rough set theory focuses on the meaning and interpretation of concepts, while algorithms to compute those concepts are studied in the computational formulation. However, the research on the former is rather limited. In this paper, we focus on a semantically sound approach of Pawlak’s rough set model and covering-based rough set models. Furthermore, we illustrate that the dominance-based rough set model can be rephrased using this semantic approach.

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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. D’eer, L., Restrepo, M., Cornelis, C., Gómez, J.: Neighborhood operators for covering based rough sets. J. Inf. Sci. 336, 21–44 (2016)

    Article  Google Scholar 

  2. Greco, S., Matarazzo, B., Słowiński, R.: Rough sets theory for multi-criteria decision analysis. Eur. J. Oper. Res. 129(1), 1–47 (2001)

    Article  MATH  Google Scholar 

  3. Greco, S., Matarazzo, B., Słowiński, R.: Multicriteria classification by dominance-based rough set approach. In: Kloesgen, W., Zytkow, J. (eds.) Handbook of Data Mining and Knowledge Discovery. Oxford University Press, New York (2002)

    Google Scholar 

  4. Grzymala-Busse, J.W.: Rule induction from rough approximations. In: Kacprzyk, J., Pedrycz, W. (eds.) Springer Handbook of Computational Intelligence, pp. 371–385. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  5. Kondo, M.: On the structure of generalized rough sets. Inf. Sci. 176, 586–600 (2006)

    Article  MathSciNet  Google Scholar 

  6. Marek, V.W., Pawlak, Z.: Information storage and retrieval systems: mathematical foundations. Theor. Comput. Sci. 1, 331–354 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  7. Marek, V.W., Truszczyński, M.: Contributions to the theory of rough sets. Fundamenta Informaticae 39, 389–409 (1999)

    MathSciNet  MATH  Google Scholar 

  8. Nguyen, H.S.: Approximate boolean reasoning: foundations and applications in data mining. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets V. LNCS, vol. 4100, pp. 334–506. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Pawlak, Z.: Mathematical Foundations of Information Retrieval, Research Report CC PAS Report 101. Computation Center, Polish Academy of Sciences (1973)

    Google Scholar 

  10. Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11(5), 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  12. Pomykala, J.A.: Approximation operations in approximation space. Bulletin de la Académie Polonaise des Sciences 35(9–10), 653–662 (1987)

    MathSciNet  MATH  Google Scholar 

  13. Qin, K., Yang, J., Pei, Z.: Generalized rough sets based on reflexive and transitive relations. Inf. Sci. 178, 4138–4141 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  15. Restrepo, M., Cornelis, C., Gómez, J.: Partial order relation for approximation operators in covering-based rough sets. Inf. Sci. 284, 44–59 (2014)

    Article  MathSciNet  Google Scholar 

  16. Rissanen, J.: Minimum-Description-Length Principle. Wiley, New York (1985)

    Google Scholar 

  17. Słowiński, R., Vanderpooten, D.: A generalized definition of rough approximation based on similarity. IEEE Trans. Knowl. Data Eng. 12, 331–336 (2000)

    Article  Google Scholar 

  18. Słowiński, R., Greco, S., Matarazzo, B.: Rough set based decision support. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, pp. 475–527. Springer, New York (2005)

    Google Scholar 

  19. Stepaniuk, J., Skowron, A.: Tolerance approximation spaces. Fundamenta Informaticae 27(2–3), 245–253 (1996)

    MathSciNet  MATH  Google Scholar 

  20. Tsang E., Chen D., Lee J., Yeung D.S.: On the upper approximations of covering generalized rough sets. In: Proceedings of the 3rd International Conference on Machine Learning and Cybernetics, pp. 4200–4203 (2004)

    Google Scholar 

  21. Wu, W.Z., Zhang, W.X.: Neighborhood operators systems and approximations. Inf. Sci. 144, 201–207 (2002)

    Article  MATH  Google Scholar 

  22. Xu, Z., Wang, Q.: On the properties of covering rough sets model. J. Henan Norm. Univ. (Natural Science) 33(1), 130–132 (2005)

    MathSciNet  MATH  Google Scholar 

  23. Xu, W., Zhang, W.: Measuring roughness of generalized rough sets induced by a covering. Fuzzy Sets Syst. 158, 2443–2455 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  24. Yao, Y.: Relational Interpretations of neighborhood operators and rough set approximation operators. Inf. Sci. 101, 21–47 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  25. Yao, Y., Zhou, B.: A logic language of granular computing. In: Proceedings of the 6th IEEE International Conference on Cognitive Informatics, pp. 178–185 (2007)

    Google Scholar 

  26. Yao, 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 

  27. Yao, Y., Yao, B.: Covering based rough sets approximations. Inf. Sci. 200, 91–107 (2012)

    Article  MATH  Google Scholar 

  28. Yao, Y., Zhang, N., Miao, D., Xu, F.: Set-theoretic approaches to granular computing. Fundamenta Informaticae 115(2–3), 247–264 (2012)

    MathSciNet  MATH  Google Scholar 

  29. Yao, Y.: The two sides of the theory of rough sets. Knowl. Based Syst. 80, 67–77 (2015)

    Article  Google Scholar 

  30. Źakowski, W.: Approximations in the space \((u,\pi )\). Demonstratio Mathematica 16, 761–769 (1983)

    MathSciNet  MATH  Google Scholar 

  31. Zhu, W., Wang, F.: Reduction and axiomatization of covering generalized rough sets. Inf. Sci. 152, 217–230 (2003)

    Article  MATH  Google Scholar 

  32. Zhu, W.: Properties of the first type of covering-based rough sets. In: Sixth IEEE International Conference on Data Mining - Workshops IEEE (2006)

    Google Scholar 

  33. Zhu, W.: Properties of the second type of covering-based rough sets. In: Proceedings of the IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology (2006)

    Google Scholar 

  34. Zhu, W.: Properties of the third type of covering-based rough sets. In: Sixth IEEE International Conference on Data Mining - Workshops (2006)

    Google Scholar 

  35. Zhu, W.: Properties of the fourth type of covering-based rough sets. In: Proceedings of Sixth International Conference on Hybrid Intelligence Systems, vol. 43 (2006)

    Google Scholar 

  36. Zhu, W., Wang, F.: A new type of covering rough sets. In: 3rd International IEEE Conference Intelligence Systems (2006)

    Google Scholar 

  37. Zhu, W., Wang, F.: On three types of covering based rough sets. IEEE Trans. Knowl. Data Eng. 19(8), 1131–1143 (2007)

    Article  Google Scholar 

  38. Zhu, W.: Relationship between generalized rough sets based on binary relation and covering. Inf. Sci. 179, 210–225 (2009)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

Lynn D’eer has been supported by the Ghent University Special Research Fund. This work was partially supported by the Spanish Ministry of Science and Technology under the Project TIN2014-57251-P and the Andalusian Research Plans P10-TIC-6858, P11-TIC-7765 and P12-TIC-2958.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Ghent, Belgium

    Lynn D’eer & Chris Cornelis

  2. Department of Computer Science and Artificial Intelligence, Research Center on Information and Communications Technology (CITIC-UGR), University of Granada, Granada, Spain

    Chris Cornelis

  3. Department of Computer Science, University of Regina, Regina, Canada

    Yiyu Yao

Authors
  1. Lynn D’eer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chris Cornelis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yiyu Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lynn D’eer .

Editor information

Editors and Affiliations

  1. INESC-ID,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Joao Paulo Carvalho

  2. LIP 6, Université Pierre et Marie Curie, Paris, France

    Marie-Jeanne Lesot

  3. School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Uzay Kaymak

  4. IDMEC,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Susana Vieira

  5. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  6. Iona College, Machine Intelligence Institute, New Rochelle, New York, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

D’eer, L., Cornelis, C., Yao, Y. (2016). A Semantical Approach to Rough Sets and Dominance-Based Rough Sets. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 611. Springer, Cham. https://doi.org/10.1007/978-3-319-40581-0_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-40581-0_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40580-3

  • Online ISBN: 978-3-319-40581-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation