Skip to main content

A Probabilistic Approach to Information System and Rough Set Theory

  • Conference paper
Facets of Uncertainties and Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 125))

Abstract

We propose a generalization of information systems which provides the probability of an object to take an attribute-value for an attribute. Notions of distinguishability relations and corresponding notions of approximations are proposed and studied in comparison with the existing one.

The author would like to thank the referees and editors for their valuable comments.

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 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

References

  1. Düntsch, I., Gediga, G., Orlowska, E.: Relational attribute systems II: reasoning with relations in information structures. In: J.F. Peters et al. (eds.) Transactions on Rough Sets VII, LNCS 4400, pp. 16–35. Springer-Verlag Berlin Heidelberg (2007)

    Google Scholar 

  2. Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen. Syst. 17, 191–200 (1990)

    Article  Google Scholar 

  3. Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough sets: a tutorial. In: Pal, S.K., Skowron, A. (eds.) Rough Fuzzy Hybridization: A New Trend in Decision-Making, pp. 3–98. Springer, Singapore (1999)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  5. Kryszkiewicz, M.: Rules in incomplete information systems. Inf. Sci. 113, 271–292 (1999)

    Article  MathSciNet  Google Scholar 

  6. Lin, T.Y., Yao, Y.Y.: Neighborhoods system: measure, probability and belief functions. In: Proceedings of the 4th International Workshop on Rough Sets and Fuzzy Sets and Machine Discovery, pp. 202–207. Nov 1996

    Google Scholar 

  7. Orlowska, E., Pawlak, Z.: Representation of nondeterministic information. Theor. Comput. Sci. 29, 27–39 (1984)

    Article  MathSciNet  Google Scholar 

  8. Pawlak, Z.: Systemy Informacyjne. Podstawy Teoretyczne. Wydawnictwa Naukowo-Techniczne, Warszawa (1983)

    Google Scholar 

  9. Pawlak, Z.: Rough probability. Bull. Pol. Acad. Sci. (Math) 32(9–10), 607–612 (1984)

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  11. Pomykala, J.A.: Approximation, Similarity and Rough Constructions. ILLC Pre-publication Series for Computation and Complexity Theory CT-93-07. University of Amsderdam, Amsderdam (1993)

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  13. Ślȩzak, D., Ziarko, W.: The investigation of the Bayesian rough set model. Int. J. Approx. Reason. 40, 81–91 (2005)

    Article  MathSciNet  Google Scholar 

  14. Stefanowski, J., Tsoukiàs, A.: On the extension of rough sets under incomplete information. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC ’99: Proceedings of the 7th International Workshop on New Directions in Rough Sets. Data Mining, and Granular-Soft Computing, pp. 73–81. Springer, London, UK (1999)

    Google Scholar 

  15. Vakarelov, D.: Modal logics for knowledge representation systems. Theor. Comput. Sci. 90, 433–456 (1991)

    MathSciNet  MATH  Google Scholar 

  16. Yao, Y.Y.: Probabilistic rough set approximations. Int. J. Approx. Reason. 49(2), 255–271 (2008)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Md. Aquil Khan .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer India

About this paper

Cite this paper

Khan, M.A. (2015). A Probabilistic Approach to Information System and Rough Set Theory. In: Chakraborty, M.K., Skowron, A., Maiti, M., Kar, S. (eds) Facets of Uncertainties and Applications. Springer Proceedings in Mathematics & Statistics, vol 125. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2301-6_9

Download citation

Publish with us

Policies and ethics