Skip to main content
SpringerLink
Log in
Book cover

International Conference on Rough Sets and Current Trends in Computing

RSCTC 2010: Rough Sets and Current Trends in Computing pp 227–236Cite as

A Fuzzy View on Rough Satisfiability

  • Conference paper

  • 1461 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6086))

Abstract

In the paper, several notions of rough satisfiability of formulas are recalled and discussed from the standpoint of fuzzy set theory. By doing so we aim to better understand what rough satisfiability really means and to look for schemata describing it.

This is a preview of subscription content, 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 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Banerjee, M.: Rough belief change. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets V. LNCS, vol. 4100, pp. 25–38. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  2. Drwal, G., Mrózek, A.: System RClass – software implementation of a rough classifier. In: Kłopotek, M.A., Michalewicz, M., Raś, Z.W. (eds.) Proc. 7th Int. Symp. Intelligent Information Systems (IIS 1998), Malbork, Poland, pp. 392–395. PAS Institute of Computer Science, Warsaw (1998)

    Google Scholar 

  3. Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. Journal of General Systems 17(2), 191–209 (1990)

    Article  MATH  Google Scholar 

  4. Gomolińska, A.: A graded meaning of formulas in approximation spaces. Fundamenta Informaticae 60(1-4), 159–172 (2004)

    MATH  MathSciNet  Google Scholar 

  5. Gomolińska, A.: Satisfiability and meaning of formulas and sets of formulas in approximation spaces. Fundamenta Informaticae 67(1-3), 77–92 (2005)

    MATH  MathSciNet  Google Scholar 

  6. Gomolińska, A.: On certain rough inclusion functions. In: Peters, J.F., Skowron, A., Rybiński, H. (eds.) Transactions on Rough Sets IX. LNCS, vol. 5390, pp. 35–55. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  7. Gomolińska, A.: Rough approximation based on weak q-RIFs. In: Peters, J.F., Skowron, A., Wolski, M., Chakraborty, M.K., Wu, W.-Z. (eds.) Transactions on Rough Sets X. LNCS, vol. 5656, pp. 117–135. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Greco, S., Matarazzo, B., Słowiński, R.: Handling missing values in rough set analysis of multi-attribute and multi-criteria decision problems. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 146–157. Springer, Heidelberg (1999)

    Google Scholar 

  9. Grzymała-Busse, J.W.: Characteristic relations for incomplete data: A generalization of the indiscernibility relation. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets IV. LNCS, vol. 3700, pp. 58–68. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Klir, G.J., Wierman, M.J.: Uncertainty-based Information: Elements of Generalized Information Theory. Physica-Verlag, Heidelberg (1998)

    MATH  Google Scholar 

  11. Kryszkiewicz, M.: Rough set approach to incomplete information system. Information Sciences 112, 39–49 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. Nakamura, A.: Fuzzy rough sets. Note on Multiple-Valued Logic in Japan 9(8), 1–8 (1988)

    Google Scholar 

  13. Pal, S.K., Skowron, A. (eds.): Rough-Fuzzy Hybridization: A New Trend in Decision Making. Springer, Singapore (1999)

    MATH  Google Scholar 

  14. Pawlak, Z.: Information systems – theoretical foundations. Information systems 6(3), 205–218 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  15. Pawlak, Z.: Rough sets. Int. J. Computer and Information Sciences 11, 341–356 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  16. Pawlak, Z.: Rough logic. Bull. Polish Acad. Sci. Tech. 35, 253–258 (1987)

    MATH  MathSciNet  Google Scholar 

  17. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer, Dordrecht (1991)

    MATH  Google Scholar 

  18. Pawlak, Z., Skowron, A.: Rough membership functions. In: Zadeh, L.A., Kacprzyk, J. (eds.) Fuzzy Logic for the Management of Uncertainty, pp. 251–271. John Wiley & Sons, New York (1994)

    Google Scholar 

  19. Polkowski, L.: Rough mereology in analysis of vagueness. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 197–204. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  20. Polkowski, L., Semeniuk-Polkowska, M.: On intensional aspects of concepts defined in rough set theory. In: Czaja, L., Szczuka, M. (eds.) Proc. 18th Workshop on Concurrency, Specification and Programming (CS& P 2009), Kraków Przegorzały, September 2009, vol. 2, pp. 486–497. Warsaw University (2009)

    Google Scholar 

  21. Polkowski, L., Skowron, A.: Rough mereology: A new paradigm for approximate reasoning. Int. J. Approximated Reasoning 15(4), 333–365 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  22. Polkowski, L., Tsumoto, S., Lin, T.Y. (eds.): Rough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems. Physica-Verlag, Heidelberg (2001)

    MATH  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  24. Słowiński, R., Greco, S., Matarazzo, B.: Dominance-based rough set approach to reasoning about ordinal data. In: Kryszkiewicz, M., Peters, J.F., Rybiński, H., Skowron, A. (eds.) RSEISP 2007. LNCS (LNAI), vol. 4585, pp. 5–11. Springer, Heidelberg (2007)

    Google Scholar 

  25. Słowiński, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations. In: Wang, P.P. (ed.) Advances in Machine Intelligence and Soft Computing, vol. 4, pp. 17–33. Duke University Press, Durham (1997)

    Google Scholar 

  26. Stepaniuk, J.: Knowledge discovery by application of rough set models. In: [26], pp. 137–233 (2001)

    Google Scholar 

  27. Xu, Z.B., Liang, J.Y., Dang, C.Y., Chin, K.S.: Inclusion degree: A perspective on measures for rough set data analysis. Information Sciences 141, 227–236 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  28. Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. Int. J. of Man–Machine Studies 37(6), 793–809 (1992)

    Article  Google Scholar 

  29. Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  30. Zadeh, L.A.: Outline of a new approach to the analysis of complex system and decision processes. IEEE Trans. on Systems, Man, and Cybernetics 3, 28–44 (1973)

    MATH  MathSciNet  Google Scholar 

  31. Ziarko, W.: Variable precision rough set model. J. Computer and System Sciences 46(1), 39–59 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  32. Ziarko, W.: Probabilistic rough sets. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 283–293. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Białystok University, Akademicka 2, 15267, Białystok, Poland

    Anna Gomolińska

Authors
  1. Anna Gomolińska
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Marcin Szczuka

  2. ICS, Warsaw University of Technology,,  

    Marzena Kryszkiewicz

  3. Department of Applied Computer Science, University of Winnipeg, R3B 2E9, Winnipeg, Manitoba, Canada

    Sheela Ramanna

  4. Dept. of Computer Science, The University of Wales, Aberystwyth, UK

    Richard Jensen

  5. Harbin Institute of Technology, PO Box 458, 150006, Harbin, China

    Qinghua Hu

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gomolińska, A. (2010). A Fuzzy View on Rough Satisfiability. In: Szczuka, M., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds) Rough Sets and Current Trends in Computing. RSCTC 2010. Lecture Notes in Computer Science(), vol 6086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13529-3_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-13529-3_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13528-6

  • Online ISBN: 978-3-642-13529-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation