Skip to main content

Oppositions in Rough Set Theory

  • Conference paper
Rough Sets and Knowledge Technology (RSKT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7414))

Included in the following conference series:

Abstract

The role of opposition in rough set theory is laid bare. There are two sources which generate oppositions in rough sets: approximations and relations. In the former case, we outline a hexagon and a cube of oppositions. In the second case, we define a classical square of oppositions and also a tetrahedron when considering the standpoint of two agents.

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

Access this chapter

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. Béziau, J.Y., Gan-Krzywoszyńska, K. (eds.): The Square of Opposition (2010), http://www.square-of-opposition.org/Square2010-handbook.pdf

  2. Béziau, J.Y., Payette, G.: Preface. Special issue on the square of opposition. Logica Universalis 2, 1 (2008)

    Article  MathSciNet  Google Scholar 

  3. Béziau, J.Y., Payette, G. (eds.): Handbook of the Second World Congress on the Square of Opposition. Peter Lang, Pieterlen (2012)

    Google Scholar 

  4. Blanché, R.: Sur l’opposition des concepts. Theoria 19, 89–130 (1953)

    Article  Google Scholar 

  5. Cattaneo, G.: Generalized rough sets (preclusivity fuzzy-intuitionistic BZ lattices). Studia Logica 58, 47–77 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ciucci, D.: Approximation algebra and framework. Fundamenta Informaticae 94(2), 147–161 (2009)

    MathSciNet  MATH  Google Scholar 

  7. Ciucci, D.: Orthopairs: A simple and widely usedway to model uncertainty. Fundamenta Informaticae 108(3-4), 287–304 (2011)

    MathSciNet  MATH  Google Scholar 

  8. Dubois, D., Prade, H.: Putting rough sets and fuzzy sets together. In: Słowinski, R. (ed.) Intelligent Decision Support – Handbook of Applications and Advances of the Rough Sets Theory, pp. 203–232. Kluwer Academic Publishers, Dordrecht (1992)

    Google Scholar 

  9. Dubois, D., Prade, H.: From Blanché hexagonal organization of concepts to formal concept analysis and possibility theory. Logica Universalis, 1–21 (in press, 2012), http://dx.doi.org/10.1007/s11787-011-0039-0

  10. Katzberg, J., Ziarko, W.: Variable precision extension of rough sets. Fundamenta Informaticae 27, 155–168 (1996)

    MathSciNet  MATH  Google Scholar 

  11. Khan, M. A., Banerjee, M.: A Study of Multiple-Source Approximation Systems. In: Peters, J.F., Skowron, A., Słowiński, R., Lingras, P., Miao, D., Tsumoto, S. (eds.) Transactions on Rough Sets XII. LNCS, vol. 6190, pp. 46–75. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  12. Lin, T.Y., Huang, K.J., Liu, Q., Chen, W.: Rough sets, neighborhood systems and approximation. In: Proceedings of the Fifth International Symposium on Methodologies of Intelligent Systems, Selected Papers, pp. 130–141 (1990)

    Google Scholar 

  13. Pawlak, Z.: Information systems - theoretical foundations. Information Systems 6, 205–218 (1981)

    Article  MATH  Google Scholar 

  14. Pawlak, Z., Skowron, A.: Rudiments of rough sets. Information Sciences 177, 3–27 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Radzikowska, A., Kerre, E.: A comparative study of fuzzy rough sets. Fuzzy Sets and Systems 126, 137–155 (2002)

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  17. Słowinski, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations. In: Wang, P. (ed.) Advances in Machine Intelligence and Soft-Computing, vol. IV, pp. 17–33. Duke University Press, Durham (1997)

    Google Scholar 

  18. Yao, J.T., Yao, Y., Ziarko, W.: Probabilistic rough sets: Approximations, decision-makings, and applications. Int. J. Approx. Reasoning 49(2), 253–254 (2008)

    Article  Google Scholar 

  19. Yao, Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences 111, 239–259 (1998)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ciucci, D., Dubois, D., Prade, H. (2012). Oppositions in Rough Set Theory. In: Li, T., et al. Rough Sets and Knowledge Technology. RSKT 2012. Lecture Notes in Computer Science(), vol 7414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31900-6_62

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31900-6_62

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31899-3

  • Online ISBN: 978-3-642-31900-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics