Skip to main content
SpringerLink
Log in
Book cover

Transactions on Rough Sets IX pp 1–13Cite as

Vagueness and Roughness

  • Chapter

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 5390))

Abstract

The paper proposes a new formal approach to vagueness and vague sets taking inspirations from Pawlak’s rough set theory. Following a brief introduction to the problem of vagueness, an approach to conceptualization and representation of vague knowledge is presented from a number of different perspectives: those of logic, set theory, algebra, and computer science. The central notion of the vague set, in relation to the rough set, is defined as a family of sets approximated by the so called lower and upper limits. The family is simultaneously considered as a family of all denotations of sharp terms representing a suitable vague term, from the agent’s point of view. Some algebraic operations on vague sets and their properties are defined. Some important conditions concerning the membership relation for vague sets, in connection to Blizard’s multisets and Zadeh’s fuzzy sets, are established as well. A classical outlook on a logic of vague sentences (vague logic) based on vague sets is also discussed.

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. Blizard, W.D.: Multiset Theory. Notre Dame J. Formal Logic 30(1), 36–66 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bonikowski, Z.: A Certain Conception of the Calculus of Rough Sets. Notre Dame J. Formal Logic 33, 412–421 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bonikowski, Z.: Sets Approximated by Representations (in Polish, the doctoral dissertation prepared under the supervision of Prof. U.Wybraniec-Skardowska), Warszawa (1996)

    Google Scholar 

  4. Bonikowski, Z., Wybraniec-Skardowska, U.: Rough Sets and Vague Sets. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds.) RSEISP 2007. LNCS, vol. 4585, pp. 122–132. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  5. Bonissone, P., Tong, R.: Editorial: reasoning with uncertainty in expert systems. Int. J. Man–Machine Studies 22, 241–250 (1985)

    Article  Google Scholar 

  6. Codd, E.F.: A Relational Model of Data for Large Shared Data Banks. Comm. ACM 13, 377–387 (1970)

    Article  MATH  Google Scholar 

  7. Cresswell, M.J.: Logics and Languages. Methuen, London (1973)

    MATH  Google Scholar 

  8. Demri, S., Orłowska, E.: Incomplete Information: Structure, Inference, Complexity. Springer, Heidelberg (2002)

    Book  MATH  Google Scholar 

  9. Fine, K.: Vagueness, Truth and Logic. Synthese 30, 265–300 (1975)

    Article  MATH  Google Scholar 

  10. Iwiński, T.: Algebraic Approach to Rough Sets. Bull. Pol. Acad. Sci. Math. 35, 673–683 (1987)

    MathSciNet  MATH  Google Scholar 

  11. Malinowski, G.: Many-Valued Logics. Oxford University Press, Oxford (1993)

    MATH  Google Scholar 

  12. Marcus, S.: A Typology of Imprecision. In: Brainstorming Workshop on Uncertainty in Membrane Computing Proceedings, Palma de Mallorca, pp. 169–191 (2004)

    Google Scholar 

  13. Marek, W., Pawlak, Z.: Rough Sets and Information Systems, ICS PAS Report 441 (1981)

    Google Scholar 

  14. Pagliani, P.: Rough Set Theory and Logic-Algebraic Structures. In: Orłowska, E. (ed.) Incomplete Information: Rough Set Analysis, pp. 109–190. Physica Verlag, Heidelberg (1998)

    Chapter  Google Scholar 

  15. Parsons, S.: Current approaches to handling imperfect information in data and knowledge bases. IEEE Trans. Knowl. Data Eng. 8(3), 353–372 (1996)

    Article  Google Scholar 

  16. Pawlak, Z.: Information Systems, ICS PAS Report 338 (1979)

    Google Scholar 

  17. Pawlak, Z.: Information Systems – Theoretical Foundations (in Polish). PWN – Polish Scientific Publishers, Warsaw (1981)

    MATH  Google Scholar 

  18. Pawlak, Z.: Information Systems – Theoretical Foundations. Information Systems 6, 205–218 (1981)

    Article  MATH  Google Scholar 

  19. Pawlak, Z.: Rough Sets. Intern. J. Comp. Inform. Sci. 11, 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  21. Pawlak, Z.: Vagueness and uncertainty: A rough set perspective. Computat. Intelligence 11(2), 227–232 (1995)

    Article  MathSciNet  Google Scholar 

  22. Pawlak, Z.: Orthodox and Non-orthodox Sets - some Philosophical Remarks. Found. Comput. Decision Sci. 30(2), 133–140 (2005)

    Google Scholar 

  23. Pomykała, J., Pomykała, J.A.: The Stone Algebra of Rough Sets. Bull. Pol. Acad. Sci. Math. 36, 495–508 (1988)

    MathSciNet  MATH  Google Scholar 

  24. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  25. Skowron, A., Komorowski, J., Pawlak, Z., Polkowski, L.: Rough Sets Perspective on Data and Knowledge. In: Klösgen, W., Żytkow, J.M. (eds.) Handbook of Data Mining and Knowlewdge Discovery, pp. 134–149. Oxford University Press, Oxford (2002)

    Google Scholar 

  26. Słowiński, R., Stefanowski, J.: Rough-Set Reasoning about Uncertain Data. Fund. Inform. 23(2–3), 229–244 (1996)

    MathSciNet  MATH  Google Scholar 

  27. Wybraniec-Skardowska, U.: Knowledge, Vagueness and Logic. Int. J. Appl. Math. Comput. Sci. 11, 719–737 (2001)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  29. Zadeh, L.A.: PRUF: A meaning representation language for natural languages. Int. J. Man–Machine Studies 10, 395–460 (1978)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Informatics, University of Opole, Opole, Poland

    Zbigniew Bonikowski

  2. Autonomous Section of Applied Logic, Poznań School of Banking, Faculty in Chorzów, Poland

    Urszula Wybraniec-Skardowska

Authors
  1. Zbigniew Bonikowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Urszula Wybraniec-Skardowska
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

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

    Andrzej Skowron

  3. Institute of Computer Science, Warsaw University of Technology, Nowowoiejska 15/19, 00-665, Warsaw, Poland

    Henryk Rybiński

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Bonikowski, Z., Wybraniec-Skardowska, U. (2008). Vagueness and Roughness. In: Peters, J.F., Skowron, A., Rybiński, H. (eds) Transactions on Rough Sets IX. Lecture Notes in Computer Science, vol 5390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89876-4_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-89876-4_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89875-7

  • Online ISBN: 978-3-540-89876-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation