Skip to main content

A Formal Study of a Generalized Rough Set Model Based on Relative Approximations

  • Conference paper
  • First Online:
Rough Sets (IJCRS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11103))

Included in the following conference series:

Abstract

We propose a generalization of the rough set model where approximation operators are defined relative to a given collection of subsets of the domain of objects. A modal logic with semantics based on relative accessibility relations is also proposed, that can be used to reason about the proposed approximations.

V. S. Patel—This work has been supported by the Council of Scientific and Industrial Research (CSIR) India, Research Grant No. 09/1022(0028)/2016-EMR-I.

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 EPUB and 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

References

  1. Balbiani, P.: Axiomatization of logics based on Kripke models with relative accessibility relations. In: Orłowska, E. (ed.) Incomplete Information: Rough Set Analysis, pp. 553–578. Physica Verlag, Heidelberg, New York (1998)

    Chapter  Google Scholar 

  2. Balbiani, P., Orłowska, E.: A hierarchy of modal logics with relative accessibility relations. J. Appl. Non-Class. Log. 9(2–3), 303–328 (1999)

    Article  MathSciNet  Google Scholar 

  3. Banerjee, M., Khan, M.A.: Propositional logics from rough set theory. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J., Orłowska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI. LNCS, vol. 4374, pp. 1–25. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71200-8_1

    Chapter  Google Scholar 

  4. Demri, S., Orłowska, E.: Incomplete Information: Structure, Inference, Complexity. Springer, Heidelberg (2002). https://doi.org/10.1007/978-3-662-04997-6

    Book  MATH  Google Scholar 

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

    Article  Google Scholar 

  6. Farinas Del Cerro, L., Orłowska, E.: \({DAL}\) - a logic for data analysis. Theor. Comput. Sci. 36, 251–264 (1985)

    Article  MathSciNet  Google Scholar 

  7. Khan, M.A.: A probabilistic approach to rough set theory with modal logic perspective. Inf. Sci. 406–407, 170–184 (2017)

    Article  Google Scholar 

  8. 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 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  11. 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. 202–208, November 1996

    Google Scholar 

  12. Orłowska, E.: Kripke semantics for knowledge representation logics. Studia Logica 49, 255–272 (1990)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  14. J. A. Pomykała. Approximation, similarity and rough constructions. ILLC prepublication series for computation and complexity theory CT-93-07, University of Amsterdam (1993)

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  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 authors

Correspondence to Md. Aquil Khan or Vineeta Singh Patel .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Khan, M.A., Patel, V.S. (2018). A Formal Study of a Generalized Rough Set Model Based on Relative Approximations. In: Nguyen, H., Ha, QT., Li, T., Przybyła-Kasperek, M. (eds) Rough Sets. IJCRS 2018. Lecture Notes in Computer Science(), vol 11103. Springer, Cham. https://doi.org/10.1007/978-3-319-99368-3_39

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-99368-3_39

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99367-6

  • Online ISBN: 978-3-319-99368-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics