Fuzziness and Ambiguity in Multi-Scale Analysis of Landscape Morphometry

  • Peter Fisher
  • Jo Wood
  • Tao Cheng


Recent research on the identification of landscape morphometric units has recognised that those units have a vague spatial extent which may be modelled by fuzzy sets. To date most such have looked at the landscape at a single resolution although scale dependence is one of the reasons the concepts are vague. The fact is that the allocation of landscape elements to morphometric classes is ambiguous, and in this chapter we exploit the ambiguity of multi-resolution classification as the basis of the morphometric classes as fuzzy sets. We explore this idea with respect to both the mountains around Ben Nevis in Scotland and the dynamic environment of a coastal dunefield. The results in the first example show that the landscape elements identified correspond to landmarks named in a placename database of the area, although many more peaks are found than are named in the available database. In the second case multi-temporal data on a dynamic coastal dunefield is used to show results for fuzzy set and fuzzy logic analysis to identify patterns of change which contrast with more traditional change analysis. Both examples provide new insights over the types of analysis which are currently available in Geographical Information Systems, and the manipulation of scale to parameterise membership of the fuzzy set is a uniquely geographical method in fuzzy set theory.


Digital Elevation Model Multiscale Analysis Dune Slack Ordnance Survey Vague Object 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bearhop DA (1997) Munro’s Tables. Scottish Mountaineering ClubGoogle Scholar
  2. Bennett, D (ed) (1999) The Munros: Hillwalker’s Guide Volume 1. Scottish Mountaineering ClubGoogle Scholar
  3. Burgess JA (1990) The sorites paradox and higher-order vagueness. Synthese 85:417–474CrossRefGoogle Scholar
  4. Burrough PA van Gaans PFM, and MacMillan RA (2000) High-resolution landform classification using fuzzy k-means. Fuzzy Sets and Systems 113: 37–52CrossRefGoogle Scholar
  5. Burrough PA, Wilson JP, van Gaans PFM, and Hansen AJ (2001) Fuzzy k-means classification of topo-climatic data as an aid to forest mapping in the Greater Yellowstone Area, USA. Landscape Ecology 16:523–546CrossRefGoogle Scholar
  6. Cheng T and Molenaar M (1999a) Objects with fuzzy spatial extent. Photogrammetric Engineering and Remote Sensing 63:403–414Google Scholar
  7. Cheng T and Molenaar M (1999b) Diachronic analysis of fuzzy objects. GeoInformatica 3: 337–356.CrossRefGoogle Scholar
  8. Collins (1998) Munro Map: All Scotland’s mountains over 3000 feet. Harper Collins Publishers, London.Google Scholar
  9. Eastman JR (1999) Idrisi32, Reference Guide Clark University, Worcester.Google Scholar
  10. Evans IS (1980) An integrated system of terrain analysis and slope mapping. Zeitschrift fur Geomorphologie Suppl-Bd: 36 274–295Google Scholar
  11. Fisher, PF (1996) Propagating effects of database generalization on the viewshed. Transactions in GIS 1(2): 69–81Google Scholar
  12. Fisher PF (2000a) Fuzzy modeling. In Openshaw S, Abrahart R and Harris T (eds) Geocomputting, Taylor & Francis, London, pp 161–186Google Scholar
  13. Fisher PF (2000b) Sorites paradox and vague geographies. Fuzzy Sets and Systems 113:7–18CrossRefGoogle Scholar
  14. Fisher PF and Wood J (1998) What is a mountain? or the Englishman who went up a Boolean geographical concept and realised it was fuzzy. Geography 83:247–256Google Scholar
  15. Fisher PF, Wood J and Cheng T (2004) Where is Helvellyn? Fuzziness of multiscale landscape morphometry. Transactions of the Institute of British Geographers 29: 106–128CrossRefGoogle Scholar
  16. Gale S (1972) Inexactness fuzzy sets and the foundation of behavioral geography. Geographical Analysis 4: 337–349Google Scholar
  17. Irvin BJ, Ventura SJ and Slater BK (1997) Fuzzy and isodata classification of landform elements from digital terrain data in Pleasant Valley, Wisconsin. Geoderma 77: 137–154CrossRefGoogle Scholar
  18. Klir GJ and Yuan B (1995) Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, Englewood CliffGoogle Scholar
  19. Kruse R, Gebhardt J and Klawonn F (1994) Foundations of Fuzzy Systems, John Wiley and Son, ChichesterGoogle Scholar
  20. MacMillan RA, Pettapiece WW, Nolan SC and Goddard T W (2000) A generic procedure for automatically segmenting landforms into oandform elements using DEMs, heuristic rules and fuzzy logic. Fuzzy Sets and Systems 113: 81–109CrossRefGoogle Scholar
  21. Ordnance Survey (1998) The English Lakes: South Western area, Coniston, Ulverston and Barrow-in-Furness. 1:25,000 Outdoor Leisure 6. Ordnance Survey, SouthamptonGoogle Scholar
  22. Peucker TK and Douglas DH (1974) Detection of surface specific points by local parallel processing of discrete terrain elevation data. Computer Graphics and Image Processing 4: 375–387Google Scholar
  23. Robinson VB (1988) Some implications of fuzzy set theory applied to geographic databases. Computers, Environment and Urban Systems 12: 89–97CrossRefGoogle Scholar
  24. Sainsbury RM (1989) What is a vague object? Analysis 49: 99–103Google Scholar
  25. Sainsbury RM (1995) Paradoxes 2nd Edition, University Press, CambridgeGoogle Scholar
  26. Seymour, J (2003) GB Waypoints: Munros. Accessed 20 April 2003Google Scholar
  27. Tate N and Wood J (2001) Fractals and scale dependencies in topography. In Tate N and Atkinson P (eds) Modelling Scale in Geographical Information Science, Wiley, Chichester, pp 35–51Google Scholar
  28. Usery EL (1996) A conceptual framework and fuzzy set implementation for geographic features. In Burrough PA and Frank A (eds) Geographic Objects with Indeterminate Boundaries, Taylor & Francis, London, pp 87–94Google Scholar
  29. Varzi AC 2001 Vagueness in Geography Philosophy and Geography 4 49–65Google Scholar
  30. Williamson T (1994) Vagueness. Routledge, LondonGoogle Scholar
  31. Wood J (1996a) Scale-based characterisation of digital elevation models. In Parker D (ed) Innovations in GIS 3, Taylor & Francis, London, pp 163–175Google Scholar
  32. Wood J (1996b) The Geomorphological Characterisation of Digital Elevation Models. Unpublished PhD Thesis, Department of Geography, University of Leicester. ( Accessed 13 September 2002Google Scholar
  33. Wood J (1998) Modelling the continuity of surface form using digital elevation models. In: Proceedings of the 8th International Symposium on Spatial Data Handling, Simon Fraser University, Burnaby, British Columbia, pp 725–736Google Scholar
  34. Wood J (2002a) Landserf: Visualisation and Analysis of Terrain Models, URL: Accessed 13 September 2002Google Scholar
  35. Wood J (2002b) Visualizing the structure and scale dependency of landscapes. In: Fisher P and Unwin D (eds), Virtual Reality in Geography, Taylor & Francis, London, pp 163–174Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Peter Fisher
    • 1
  • Jo Wood
    • 2
  • Tao Cheng
    • 3
  1. 1.Department of GeographyUniversity of LeicesterLeicesterUK
  2. 2.School of InformaticsCity UniversityLondonUK
  3. 3.Department of Land Surveying and Geo-InformaticsThe Hong Kong Polytechnic UniversityKowloon, Hong Kong

Personalised recommendations