Skip to main content
SpringerLink
Log in

Geometric Type-2 Fuzzy Sets

  • Chapter
  • First Online:
Advances in Type-2 Fuzzy Sets and Systems

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 301))

Abstract

This chapter gives a review and technical overview of the geometric representation of a type-2 fuzzy set and explores logical operators used to manipulate this representation. Geometric fuzzy logic provides a distinct way of understanding a fuzzy system, where fuzzy sets and fuzzy logic operators are seen purely as geometric objects which are manipulated only using knowledge of geometry. This approach is simple and intuitive, ideal for those who are not well versed in discrete mathematics. For researchers working with fuzzy systems regularly, this approach can raise some interesting questions about how fuzzy sets and systems are constructed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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. Bashein, G., Detmer, P.R.: Centroid of a Polygon. In: Heckbert, P.S. (ed.) Graphics Gems IV, pp. 3–6. Academic Press, Massachusetts (1994)

    Google Scholar 

  2. Bentley, J.L., Ottmann, T.A.: Algorithms for reporting and counting geometric intersections. IEEE Trans. Comput. 28(9), 643–647 (1979)

    Article  MATH  Google Scholar 

  3. Bourke, P.: Calculating the area and centroid of a polygon). http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline/polyarea/ or on CDROM from http://local.wasp.uwa.edu.au/~pbourke/. July 1988

  4. Coupland, S.: Type-2 fuzzy sets: geometric defuzzification and type-reduction. In: Proceedings of the IEEE Symposium on Foundations of Computational Intelligence, Honolulu, Hawaii, pp. 622–629, April 2007

    Google Scholar 

  5. Coupland, S., John, R.: A new and efficient method for the type-2 meet operation. In: Proceedings of FUZZ-IEEE 2004, Budapest, Hungary, pp. 959–964, July 2004

    Google Scholar 

  6. Coupland, S., John, R.: Fuzzy logic and computational geometry. In: Proceedings of RASC 2004, Nottingham, England, pp. 3–8, Dec 2004

    Google Scholar 

  7. Coupland, S., John, R.: A fast geometric method for defuzzification of type-2 fuzzy sets. IEEE Trans. Fuzzy Syst. 16(4), 929–941 (2008)

    Article  Google Scholar 

  8. Coupland, S., John, R.: New geometric inference techniques for type-2 fuzzy sets. Int. J. Approx. Reason. 49(1), 198–211 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Guigue, P., Devillers, O.: Fast and robust triangle-triangle overlap test using orientation predicates. J. Graph. Tools 8(1), 25–32 (2003)

    Google Scholar 

  10. Hamrawi, H., Coupland, S., John, R.: A novel alpha-cut representation for type-2 fuzzy sets. In: FUZZ IEEE 2010 (WCCI 2010), IEEE, Barcelona, Spain, IEEE, pp. 1–8, July 2010

    Google Scholar 

  11. Karnik, N.N., Mendel, J.M.: Operations on type-2 fuzzy sets. Fuzzy Sets Syst. 122, 327–348 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mendel, J.M., Liu, F., Zhai, D.: Alpha-plane representation for type-2 fuzzy sets: theory and applications. IEEE Trans. Fuzzy Syst. 17, 1189–1207 (October 2009)

    Article  Google Scholar 

  13. Möller, T.: A fast triangle-triangle intersection test. J. Graph. Tools 2(2), 25–30 (1997)

    Article  Google Scholar 

  14. Wagner, C., Hagras, H.: Toward general type-2 fuzzy logic systems based on zslices. IEEE Trans. Fuzzy Syst. 18(4), 637–660 (Aug. 2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. De Montfort University, The Gateway, Leicester, LE1 9BH, UK

    Simon Coupland

  2. University of Nottingham, Wollaton Road, Nottingham, NG8 1BB, UK

    Robert John

Authors
  1. Simon Coupland
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert John
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Simon Coupland .

Editor information

Editors and Affiliations

  1. Ryerson University, Victoria Street 350, Toronto, M5B 2K3, Ontario, Canada

    Alireza Sadeghian

  2. Hughes Aircraft Electrical Engineering B, Department of Electrical Engineering - S, University of Southern California, 3740 McClintock Ave., Los Angeles, 90089-2564, California, USA

    Jerry M. Mendel

  3. Ryerson University, Victoria Street 350, Toronto, M5B 2K3, Ontario, Canada

    Hooman Tahayori

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Coupland, S., John, R. (2013). Geometric Type-2 Fuzzy Sets. In: Sadeghian, A., Mendel, J., Tahayori, H. (eds) Advances in Type-2 Fuzzy Sets and Systems. Studies in Fuzziness and Soft Computing, vol 301. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6666-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-6666-6_6

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-6665-9

  • Online ISBN: 978-1-4614-6666-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation