Skip to main content

Higher Reasoning with Level-2 Fuzzy Regions

  • Conference paper
  • 604 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7022))

Abstract

Spatial data is quite often is prone to uncertainty and imprecision. For this purpose, fuzzy regions have been developed: they basically consist of a fuzzy set over a two dimensional domain, allowing for both fuzzy regions and fuzzy points to be modelled. The model is extended to a level-2 fuzzy region to overcome some limitations, but this has an impact on operations. In this contribution, we will look into the construction of and combination of existing data to yield level-2 fuzzy regions.

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

Buying options

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 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Clementini, E., Di Felice, P.: An algebraic model for spatial objects with undetermined boundaries. In: GISDATA Specialist Meeting - Revised Version (1994)

    Google Scholar 

  2. Cohn, A., Gotts, N.M.: Spatial regions with undetermined boundaries. In: Proceedings of the Second ACM Workshop on Advances in GIS, pp. 52–59 (1994)

    Google Scholar 

  3. Schneider, M.: Modelling Spatial Objects with Undetermined Boundaries Using the Realm/ROSE Approach. In: Geographic Objects with Indeterminate Boundaries. GISDATA Series, vol. 2, pp. 141–152. Taylor & Francis, Abington (1996)

    Google Scholar 

  4. Kanjilal, V., Liu, H., Schneider, M.: Plateau regions: An implementation concept for fuzzy regions in spatial databases and GIS. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS(LNAI), vol. 6178, pp. 624–633. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  5. Verstraete, J., De Tré, G., De Caluwe, R., Hallez, A.: Field based methods for the modelling of fuzzy spatial data. In: Fred, P., Vince, R., Maria, C. (eds.) Fuzzy Modeling with Spatial Information for Geographic Problems, pp. 41–69. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  6. Gottwald, S.: Set theory for fuzzy sets of higher level. Fuzzy Sets and Systems 2(2), 125–151 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  7. Mendel, J.M.: Uncertain rule-based fuzzy logic systems, Introduction and new directions. Prentice Hall, Englewood Cliffs (2001)

    MATH  Google Scholar 

  8. Jörg, V.: Using level-2 fuzzy sets to combine uncertainty and imprecision in fuzzy regions. In: Mugellini, E., Szczepaniak, P.S., Pettenati, M.C., Sokhn, M. (eds.) AWIC 2011. AISC, vol. 86, pp. 163–172. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  9. Verstraete, J.: Union and intersection of level-2 fuzzy regions. In: World Conference on Soft Computing (2011)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  11. Verstraete, J., De Tré, G., Hallez, A., De Caluwe, R.: Bitmap based structures for the modelling of fuzzy entities. Control and Cybernetics 35, 147–164 (2006)

    MATH  Google Scholar 

  12. Verstraete, J., De Tré, G., Hallez, A., De Caluwe, R.: Using tin-based structures for the modelling of fuzzy gis objects in a database. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15, 1–20 (2007)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Verstraete, J. (2011). Higher Reasoning with Level-2 Fuzzy Regions. In: Christiansen, H., De Tré, G., Yazici, A., Zadrozny, S., Andreasen, T., Larsen, H.L. (eds) Flexible Query Answering Systems. FQAS 2011. Lecture Notes in Computer Science(), vol 7022. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24764-4_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24764-4_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24763-7

  • Online ISBN: 978-3-642-24764-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics