Skip to main content

Rough Temporal Vague Sets in Pawlak Approximation Space

  • Conference paper
Rough Set and Knowledge Technology (RSKT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6401))

Included in the following conference series:

  • 932 Accesses

Abstract

The combination of temporal vague set theory and rough set theory is developed in this paper. The lower and upper approximation operators of a temporal vague set are constructed, which is partitioned by an indiscernibility relation in Pawlak approximation space, and the concept of rough temporal vague sets is proposed as a generalization of rough vague sets. Further properties associated with the lower and upper approximations of temporal vague sets are studied. Finally, the roughness measure of a temporal vague set is defined as an extension of the parameterized roughness measure of a vague set. Meantime, some properties of roughness measure are established.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gau, W.L., Buehrer, D.J.: Vague sets. IEEE Transactions on Systems, Man and Cybernetics 23, 610–614 (1993)

    Article  MATH  Google Scholar 

  2. Pawlak, Z.: Rough sets. Internationtal Journal of Computer and Information Sciences 11, 341–356 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  3. Pawlak, Z.: Rough sets: Theoretical aspects of reasoning about data. Kluwer academic publishers, Dordrecht (1991)

    MATH  Google Scholar 

  4. Pawlak, Z.: Rough sets and fuzzy sets. Fuzzy Sets and Systems 17, 99–102 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  5. Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17, 191–209 (1990)

    Article  MATH  Google Scholar 

  6. Dubois, D., Prade, H.: Two fold fuzzy sets and rough sets-some issues in knowledge representation. Fuzzy Sets and Systems 23, 3–18 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  7. Wygralak, M.: Rough sets and fuzzy sets-some remarks on interrelations. Fuzzy Sets and Systems 29, 241–243 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  8. Yao, Y.Y.: A comparative study of fuzzy sets and rough sets. Information Sciences 109, 227–242 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  9. Yao, Y.Y.: Semantics of fuzzy sets in rough set theory. LNCS Transactions on Rough Sets 2, 310–331 (2004)

    Google Scholar 

  10. Yao, Y.Y.: Combination of rough and fuzzy sets based on α-level sets. In: Lin, T.Y., Cercone, N. (eds.) Rough Sets and Data Mining: Analysis for Imprecise Data, pp. 301–321. Kluwer Academic Publishers, Boston (1997)

    Google Scholar 

  11. Wang, J., Liu, S.Y., Zhang, J.: Roughness of a vague set. International Journal of Computational Cognition 3(3), 83–87 (2005)

    Google Scholar 

  12. Banerjee, M., Sankar, K.P.: Roughness of a fuzzy set. Information Sciences 93, 235–246 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  13. Eswarlal, T.: Roughness of a Boolean vague set. International Journal of Computational Cognition 6(1), 8–11 (2008)

    Google Scholar 

  14. Gu, S.M., Gao, J., Tian, X.Q.: A fuzzy measure based on variable precision rough sets. In: Cao, B.Y. (ed.) Fuzzy Information and Engineering (ICFIE). ASC, vol. 40, pp. 798–807 (2007)

    Google Scholar 

  15. Huynh, V.N., Nakamori, Y.: A roughness measure for fuzzy sets. Information Sciences 173, 255–275 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  16. Zhang, X.Y., Xu, W.H.: A Novel Approach to Roughness Measure in Fuzzy Rough Sets. Fuzzy Information and Engineering (ICFIE) ASC 40, 775–780 (2007)

    Article  Google Scholar 

  17. Pattaraintakorn, P., Naruedomkul, K., Palasit, K.: A note on the roughness measure of fuzzy sets. Applied Mathematics Letters 22, 1170–1173 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  18. Al-Rababah, A., Biswas, R.: Rough vague sets in an approximation space. International Journal of Computational Cognition 6(4), 60–63 (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Shen, Y. (2010). Rough Temporal Vague Sets in Pawlak Approximation Space. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds) Rough Set and Knowledge Technology. RSKT 2010. Lecture Notes in Computer Science(), vol 6401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16248-0_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-16248-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16247-3

  • Online ISBN: 978-3-642-16248-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics