Skip to main content
SpringerLink
Log in
Book cover

Applying Soft Computing in Defining Spatial Relations pp 179–202Cite as

A Fuzzy Set Model of Approximate Linguistic Terms in Descriptions of Binary Topological Relations Between Simple Regions

  • Chapter

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 106))

Abstract

While handling geospatial data, one often faces at least two types of fuzziness. The first type of fuzziness is found in the use of approximate linguistic terms to describe spatial objects and spatial relations. For instance, in “The flash flood in October of 1988 nearly completely flooded downtown San Marcos,” the term “nearly completely” is approximate in nature. The second type of fuzziness is due to the indeterminate nature of the boundaries of some spatial objects. Good examples of such objects are climatic regions (e.g., hot versus warm regions) and polygons showing different soil types. This chapter is only concerned with the first type of fuzziness. It develops a fuzzy set model of approximate linguistic terms used in descriptions of binary topological relations between simple regions. After discussing related work, the author reviews cognitive evidences that demonstrate the fuzziness of approximate linguistic terms. Then a fuzzy set model of three approximate linguistic terms, ‘a little bit,’ ‘somewhat,’ and ‘nearly completely,’ is presented. A discussion of possible further research is followed by a summary at the end of the chapter.

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   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
Hardcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. F. Abler. The National Science Foundation National Center for Geographic Information and Analysis. International Journal of Geographical Information Systems, 1 (4): 303–326, 1987.

    Article  Google Scholar 

  2. D. Altman. Fuzzy set theoretic approaches for handling imprecision in spatial analysis. Int. Journal of Geographical Information Systems, 8 (3): 271–289, 1994.

    Article  Google Scholar 

  3. P. A. Burrough. Fuzzy mathematical methods for soil survey and land evaluation. Journal of Soil Science, 40: 477–492, 1989.

    Article  Google Scholar 

  4. P. A. Burrough and A. U. Frank (Eds.). Geographic Objects with Indeterminate Boundaries, Taylor and Francis, London, 1996.

    Google Scholar 

  5. E. Clementine and P. Di Felice. An algebraic model for spatial objects with indeterminate boundaries. In: P. A. Burrough and A. U. Frank (Eds.), Geographic Objects with Indeterminate Boundaries, Taylor and Francis, London, pages 155–169, 1996.

    Google Scholar 

  6. E. Clementini and P. Di Felice. A model for representing topological relationships among complex geometric features in spatial databases. Information Sciences, 90: 121–136, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  7. E. Clementini and P. Di Felice. Approximate topological relations. International Journal of Approximate Reasoning, 16: 173–204, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. G. Cohn and N. M. Gotts. The ‘Egg-Yolk’ representation of regions with indeterminate boundaries. In: P. A. Burrough and A. U. Frank (Eds.), Geographic Objects with Indeterminate Boundaries, Taylor and Francis, London, pages 171–187, 1996.

    Google Scholar 

  9. D. Dubois and M.-C. Jaulent. A general approach to parameter evaluation in fuzzy digital pictures. Pattern Recognition Letters, 6: 251–259, 1987.

    Article  MATH  Google Scholar 

  10. M. J. Egenhofer and R. Franzosa. Point-set topological spatial relations. International Journal of Geographical Information Systems, 5 (2): 161–174, 1991.

    Article  Google Scholar 

  11. M. J. Egenhofer, J. Glasgow, O. Gunther, J. Herring, and D. Peuquet. Progress in Computational Methods for Representing Geographic Concepts. International Journal of Geographical Information Science, 13(8):775–796,1999.

    Google Scholar 

  12. M. J. Egenhofer and J. R. Herring. Categorizing Topological Spatial Relations Between Point, Line, and Area Objects. In: M. J. Egenhofer, D. M. Mark, and J. R. Herring, The 9-Intersection: Formalism and its Use For Natural-Language Spatial Predicates, Santa Barbara, CA: National Center for Geographic Information and Analysis, Report 94–1, 1994.

    Google Scholar 

  13. M. J. Egenhofer and D. M. Mark. Modeling conceptual neighborhoods of topological relations. Int. Journal of Geographical Information Systems, 9 (5): 555–565, 1995.

    Article  Google Scholar 

  14. M. Erwig and M. Schneider. Vague Regions. In SSD’97 (5th Int. Symp. on Advances in Spatial Databases), LNCS 1262, pages 298–320, 1997.

    Google Scholar 

  15. P. F. Fisher. First experiments in viewshed uncertainty: The accuracy of the viewable area. Photogrammetric Engineering and Remote Sensing, 57: 1321–1327, 1991.

    Google Scholar 

  16. P. F. Fisher. First experiments in viewshed uncertainty: Simulating the fuzzy viewshed. Photogrammetric Engineering and Remote Sensing, 58: 345–352, 1992.

    Google Scholar 

  17. P. F. Fisher. Algorithm and implementation uncertainty in the viewshed function. International Journal of Geographical Information Systems, 7: 331–347, 1993.

    Article  Google Scholar 

  18. J. Freeman. The modeling of spatial relations. Computer Graphics and Image Processing, 4: 156–171, 1975.

    Article  Google Scholar 

  19. N. W. Hazelton, L. Bennett, and J. Masel. Topological structures for 4-dimensional geographic information systems. Computers, Environment, and Urban Systems, 16 (3): 227–237, 1992.

    Article  Google Scholar 

  20. G. J. Klir and B. Yuan. Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, Upper Saddle River, NJ, 1995.

    Google Scholar 

  21. R. Krishnapuram, J. M. Keller, and Y. Ma. Quantitative analysis of properties and spatial relations of fuzzy image regions. IEEE Transactions on Fuzzy Systems, 1 (3): 222–233, 1993.

    Article  Google Scholar 

  22. B. Landau and R. Jackendoff. `What’ and `where’ in spatial language and spatial cognition. Behavioral and Brain Sciences, 16: 217–265, 1993.

    Article  Google Scholar 

  23. Y. Leung. Approximate characterization of some fundamental concepts of spatial analysis. Geographical Analysis, 14 (1): 29–40, 1982.

    Article  Google Scholar 

  24. Y. Leung. On the imprecision of boundaries Geographical Analysis, 19: 125–151, 1987.

    Article  Google Scholar 

  25. D. M. Mark. Languages of Spatial Relations: Researchable Questions and NCGIA Research Agenda, Santa Barbara, CA: National Center for Geographic Information and Analysis, Report 89–2A, 1989.

    Google Scholar 

  26. D. M. Mark. Spatial Representation: A Cognitive View. In: D. J. Maguire, M. F. Goodchild, D. W. Rhind, and P. Longley (Eds.), Geographical Information Systems: Principles and Applications, Second edition, John Wiley and Sons, NY, 1:81–89, 1999.

    Google Scholar 

  27. D. M. Mark and M. J. Egenhofer. Modeling spatial relations between lines and regions: combining formal mathematical models and human subjects testing. Cartography and Geographic Information Systems, 21 (4): 195–212, 1994.

    Google Scholar 

  28. D. M. Mark and M. J. Egenhofer. Topology of Prototypical Spatial Relations Between Lines and Regions in English and Spanish. In Auto Carto 12 (12th International Symposium on Computer-Assisted Cartography), pages 245–254, Charlotte, North Carolina, March 1995.

    Google Scholar 

  29. D. M. Mark and A. U. Frank (Eds.). Cognitive and Linguistic Aspects of Geographic Space, Kluwer Academic Publishers, Dordrecht, 1991.

    Google Scholar 

  30. D. M. Mark, C. Freksa, S. C. Hirtle, R. Lloyd, and B. Tversky. Cognitive Models of Geographic Space. International Journal of Geographic Information Science, 13 (8): 747–774, 1999.

    Article  Google Scholar 

  31. P. Matsakis, J. Keller, L. Wendling, J. Marjamaa, and O. Sjahputera. Linguistic Description of Relative Positions in Images. TSMC Part B (IEEE Trans. on Systems, Man and Cybernetics), 31 (4): 573–588, 2001.

    Article  Google Scholar 

  32. NCGIA (National Center for Geographic Information and Analysis). The research plan of the National Center for Geographic Information and Analysis. International Journal of Geographical Information Systems, 3 (2): 117–136, 1989.

    Article  Google Scholar 

  33. S. K. Pal and A. Ghosh. Index of area coverage of fuzzy subsets and object extraction. Pattern Recognition Letters, 11:831–841, 1990.

    Google Scholar 

  34. D. J. Peuquet. Representations of geographic space: toward a conceptual synthesis. Annals of the Association of American Geographers, 78: 375–394, 1988.

    Article  Google Scholar 

  35. D. J. Peuquet and C.-X. Zhan. An algorithm to determine the directional relationship between arbitrarily-shaped polygons in the plane. Pattern Recognition, 20: 65–74, 1987.

    Article  Google Scholar 

  36. G. Retz-Schmidt. Various views on spatial prepositions. AI Magazine, 9: 95–105, 1988.

    Google Scholar 

  37. V. B. Robinson. Implications of fuzzy set theory for geographic databases. Computers, Environment, and Urban Systems, 12: 89–98, 1988.

    Article  Google Scholar 

  38. V. B. Robinson. Interactive machine acquisition of a fuzzy spatial relation. Computers and Geosciences, 16: 857–872, 1990.

    Article  Google Scholar 

  39. V. B. Robinson, M. Blaze, and D. Thongs. Representation and acquisition of a natural language relation for spatial information retrieval. In Second International Symposium on Spatial Data Handling, pages 472–487, Seattle, Washington, 1986.

    Google Scholar 

  40. V. B. Robinson and R. Wong. Acquiring approximate representation of some spatial relations. In Auto Carto 8 (8th International Symposium on Computer-Assisted Cartography), pages 604–622, 1987.

    Google Scholar 

  41. A. Rosenfeld. Fuzzy digital topology. Information and Control, 40: 76–87, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  42. A. Rosenfeld. Fuzzy rectangles. Pattern Recognition Letters, 11: 677–679, 1990.

    Article  MATH  Google Scholar 

  43. A. Rosenfeld and R. Klette. Degree of adjacency or surroundedness. Pattern Recognition Letters, 18 (2): 169–177, 1985.

    MathSciNet  MATH  Google Scholar 

  44. A. R. Shariff, M. J. Egenhofer, and D. M. Mark. Natural-language spatial relations between linear and areal objects: the topology and metric of English-language terms. International Journal of Geographical Information Science, 11(3):215–246,1998.

    Google Scholar 

  45. L. Talmy. How language structures space. In: H. L. Pick Jr. and L. P. Acredolo (Eds.), Spatial Orientation: Theory, Research and Application, New York, Plenum, pages 225–282, 1983.

    Google Scholar 

  46. H. A. Taylor and B. Tversky. Spatial mental models derived from survey and route descriptions. Journal of Memory and Language, 31: 261–282, 1992.

    Article  Google Scholar 

  47. H. A. Taylor and B. Tversky. Perspective in spatial descriptions. Journal of Memory and Language, 35: 371–391, 1996.

    Article  Google Scholar 

  48. D. J. Unwin. Geographical information systems and the problem of ‘error and uncertainty.’ Progress in Human Geography, 19 (4): 549–558, 1995.

    Article  Google Scholar 

  49. F. Wang and G. B. Hall. Fuzzy representation of geographical boundaries in GIS. International Journal of Geographical Information Systems, 10 (5): 573–590, 1996.

    Google Scholar 

  50. F. Wang, G. B. Hall, and Subaryono. Fuzzy information representation and processing in conventional GIS software: database design and application. International Journal of Geographical Information Systems, 4: 261–283, 1990.

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  52. F. B. Zhan. Approximation of Topological Relations Between Fuzzy Regions Satisfying a Linguistically Described Query (extended abstract). In: S. C. Hirtle and A. U. Frank (Eds.), COSIT’97, Spatial Information Theory: A Theoretical Basis for GIS, LNCS 1329, pages 509–510, Laurel Highlands, Pennsylvania, USA, October 1997.

    Google Scholar 

  53. F. B. Zhan. Approximate analysis of topological relations between geographic regions with indeterminate boundaries. Soft Computing, 2 (2): 28–34, 1998.

    Article  Google Scholar 

  54. F. B. Zhan. How Much is Region Q Covering Region R `a Little Bit,’ `Somewhat,’ or `Nearly Completely?’ In: M. Cristani and B. Bennett (Eds.), SVUG01: The First COSIT (Conference on Spatial Information Theory) Workshop on Spatial Vagueness, Uncertainty and Granularity, Morro Bay, CA, September 2001.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geography, Southwest Texas State University, San Marcos, Texas, 78666, USA

    F. Benjamin Zhan

Authors
  1. F. Benjamin Zhan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. CECS Department, EBW 201, University of Missouri, 65211-2060, Columbia, MO, USA

    Pascal Matsakis

  2. CIS Department, Philadelphia University, 19144, Philadelphia, PA, USA

    Les M. Sztandera

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Physica-Verlag Heidelberg

About this chapter

Cite this chapter

Zhan, F.B. (2002). A Fuzzy Set Model of Approximate Linguistic Terms in Descriptions of Binary Topological Relations Between Simple Regions. In: Matsakis, P., Sztandera, L.M. (eds) Applying Soft Computing in Defining Spatial Relations. Studies in Fuzziness and Soft Computing, vol 106. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1752-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-7908-1752-2_8

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-00294-0

  • Online ISBN: 978-3-7908-1752-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation