Double Vagueness: Effect of Scale on the Modelling of Fuzzy Spatial Objects

  • Tao Cheng
  • Pete Fisher
  • Zhilin Li
Conference paper


In the identification of landscape features vagueness arises from the fact that the attributes and parameters that make up a landscape vary over space and scale. In most existing studies, these two kinds of vagueness are studied separately. This paper investigates their combination (double vagueness) in the identification of coastal landscape units. Fuzzy set theory is used to describe the vagueness of geomorphic features based on continuity in space. The vagueness resulting from the scale of measurement is evaluated by statistical indicators. The differences of fuzzy objects derived from data at differing resolutions are studied in order to examine these higher-order uncertainties. Multi-scale analysis of the landscape is carried out using a moving window, ranging in size from 60x60 meters to 1500x1500 meters. The statistics of the fuzziness of the fuzzy landscape units are calculated, and the variability of them with scale is assessed. It shows that a major affect of scale on the mapping of geomorphic landscape units, is determination of the area of those units. This result implies that caution must be exercised in comparing landscapes at different scales and in choosing the resolution of the data that best describes the process under study.


Uncertainty Vagueness Multiscale Fuzzy Spatial Objects 


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  1. Brassel, K. E. and Weibel, R., 1988, A Review and Conceptual Framework for Automated Map Generalisation, International Journal of Geographical Information Systems, 2, 229–244.Google Scholar
  2. Burrough, P. A., van Gaans, P. F. M., and MacMillan, R. A., 2000, High-resolution landform classification using fuzzy k-means. Fuzzy Sets and Systems, 113, 37–52.CrossRefGoogle Scholar
  3. Cheng, T., Molenaar, M. and Bouloucos, T., 1997, Identification of fuzzy objects from field observation data. In Spatial Information Theory: A Theoretical Basis for GIS, Lecture Notes in Computer Sciences, edited by S. C. Hirtle and A. U. Frank (Berlin: Spring-Verlag), Vol. 1329, pp. 241–259.Google Scholar
  4. Cheng, T. and Molenaar, M, 1999, Objects with fuzzy spatial extent. Photogrammetric Engineering and Remote Sensing, 65, 797–801.Google Scholar
  5. Cheng, T., 2002, Fuzzy spatial objects, their change and uncertainties, Photogrammetric Engineering and Remote Sensing, 68, 41–49.Google Scholar
  6. Fisher, P., Wood, J., Cheng, T., and Rogers, P., 2004, Where is Helvellyn? Fuzziness of multiscale landscape morphometry. Transactions of the Institute of British Geographers, 29, 106–128.CrossRefGoogle Scholar
  7. Foody, G. M., 2002, Status of land cover classification accuracy assessment. Remote Sensing of Environment, 80, 185–201.CrossRefGoogle Scholar
  8. Fotheringham, A. S., and Wong, D. W. S., 1991, The modifiable areal unit problem in statistical analysis, Environment and Planning, 23, 1025–1044.Google Scholar
  9. Francis, J. M. and Kopatek, J. M., 2000, Multiscale effects of grain size on land-scape pattern analysis. Geographic Information Sciences, 6, 27–37.Google Scholar
  10. Hay, G. J., Blaschke., T., Marceau, D. J., and Bouchard, A., 2003, A comparision of three image-object methods for the multiscale analysis of landscape structure. ISPRS Journal of Photogrammetry & Remote Sensing, 57, 327–345.Google Scholar
  11. He, H.S., Venturta, S. J., and Mladenoff, D.J., 2002, Effects of spatial aggregation approaches on classified satellite imagery. International Journal of Geographical Information Science, 16, 93–109.CrossRefGoogle Scholar
  12. Heuvelink, G. B. M. and Burrough, P., 2002, Developments in statistical approaches to spatial uncertainty and its Propagation, International Journal of Geographical Information Science, 16, 111–113.CrossRefGoogle Scholar
  13. Jelinski, D. E., and Wu, J., 1996, The modifiable area unit problem and implications for landscape. Landscape Ecology, 11, 129–140.Google Scholar
  14. Li, Z. L. and Openshaw, S., 1993, A natural principle for objective generalisation of digital map data. Cartography and Geographic Information System, 20, 19–29.Google Scholar
  15. Mackay, D. S., Samanta, S., Ahl, D. E., Ewers, B. E., Gower, S., and Burrows, S. N., 2003, Automated parameterization of land surface process models using fuzzy logic. Transactions in GIS, 7, 139–153.CrossRefGoogle Scholar
  16. Marceau, D. J., 1999, The scale issue in the social and natural sciences. Canadian Journal of Remote Sensing, 25, 347–356.Google Scholar
  17. McMaster, R. B. and Shea, K. S., 1992, Generalization in Digital Cartography (Association of American Geographers), 134p.Google Scholar
  18. Openshaw, S., 1983, The Modifiable Areal Unit Problem, CATMOG 38 (Norwich, UK: Geo Books).Google Scholar
  19. Robinson, V. B., 2003, A perspective on the fundamentals of fuzzy sets and their use in geographic information systems. Transactions in GIS, 7, 3–30.Google Scholar
  20. Tate, N. and Atkinson, P. (eds.)., 2001. Modelling Scale in Geographical Information Science (Chichester: Jone Wiley & Sons), 277pp.Google Scholar
  21. Usery, E. L., 1996, A conceptual framework and fuzzy set implementation for geographic feature. In Geographic Objects with Indeterminate Boundaries, edited by P. A. Burrough and A. U. Frank (London: Taylor & Francis), pp. 71–85.Google Scholar
  22. Wang, F. and Hall, G. B., 1996, Fuzzy representation of geographical boundaries in GIS, International Journal of Geographical Information Systems, 10, 573–590Google Scholar
  23. Wood, J., 1996, The Geomorphological Characterisation of Digital Elevation Models Unpublished PhD Thesis, Department of Geography, University of Leicester. (, Accessed February 2003.Google Scholar
  24. Wu, J., and Qi, Y., 2000, Dealing with scale in landscape analysis: an overview. Geographic Information Sciences, 6, 1–5.Google Scholar
  25. Wu, J., Jelinski, D. E., Luck, M. and Tueller, P.T., 2000, Multiscale analysis of landscape heterogeneity: scale variance and pattern metrics. Geographic Information Sciences, 6, 6–19.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Tao Cheng
    • 1
  • Pete Fisher
    • 2
  • Zhilin Li
    • 1
  1. 1.Department of Land Surveying and GeoInformaticsThe Hong Kong Polytechnic UniversityHung Hom, Kowloon, Hong Kong
  2. 2.Department of GeographyUniversity of LeicesterLeicesterUK

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