Modelling the Fuzzy Spatial Extent of Geographical Entities

  • Cidália Costa Fonte
  • Weldon A. Lodwick


In several situations the spatial extent of geographical entities is uncertain or fuzzy. In such cases the entities may be represented using fuzzy sets through the construction of the herein called “fuzzy geographical entities”. Four sources of fuzziness are identified in the process of constructing geographical entities characterized by predefined attributes through the classification of a tessellation. For each, a method to compute the membership grades to the fuzzy geographical entity is proposed, based on the appropriate semantic interpretation of the grades of membership. The interpretations used are the likelihood view of membership grades, the random set view and the similarity view. A practical example is presented for each case.


Membership Function Digital Elevation Model Fuzzy Number Triangular Fuzzy Number Geographical Space 
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  1. Bilgiç T, Türkşen I (2000) Measurement of Membership functions: Theoretical and empirical work. In: Dubois D, Prade H (eds) Fundamentals of Fuzzy Sets. The Handbook of Fuzzy Sets Series, Kluwer Acad. Publ., 195–230Google Scholar
  2. Burrough P, (1996) Natural Objects with Indeterminate Boundaries. In: Burrough P, Frank A (eds) Geographic Objects with Indeterminate Boundaries. Taylor & Francis, LondonGoogle Scholar
  3. Burrough P, MacDonnell R (1998) Principles of Geographical Information Systems. Oxford University Press, OxfordGoogle Scholar
  4. Cheng T, Molenaar M, Bouloucos T (1997) Identification of fuzzy objects from field observation data. In: Hirtle S C, Frank A U (eds) Proceedings of Conference of Spatial Information Theory (COSIT’97), Spatial Information Theory: A Theoretical Basis for GIS, Lecture Notes in Computer Sciences. Berlin: Spring-Verlag, 1329: 241–259Google Scholar
  5. Cheng T, Molenaar M (1999) Objects with Fuzzy Spatial Extent. Photogrammetric Engineering & Remote Sensing, 65: 797–801Google Scholar
  6. Dubois D, Prade H (1989) Fuzzy sets, probability and measurement. European Journal of Operational Research, 40: 135–154CrossRefGoogle Scholar
  7. Dubois D, Prade H (1991) Random sets and fuzzy interval analysis. Fuzzy Sets and Systems, 42: 87–101CrossRefGoogle Scholar
  8. Dubois D, Nguyen H, Prade H (2000) Possibility theory, probability and fuzzy sets. In: Dubois D, Prade H (eds) Fundamentals of Fuzzy Sets. The Handbook of Fuzzy Sets Series, Kluwer Acad. Publ., 343–438Google Scholar
  9. Dubois, D., Prade, H., (2000b), Fuzzy interval analysis. In Dubois D, Prade H (eds) Fundamentals of Fuzzy Sets. The Handbook of Fuzzy Sets Series, Kluwer Acad. Publ., 483–581.Google Scholar
  10. Fonte C (2003) Entidades Geográficas Difusas — Métodos de Construção e Processamento. Ph.D. Thesis, Coimbra UniversityGoogle Scholar
  11. Hisdal E (1988) Are grades of membership probabilities?. Fuzzy Sets and Systems 25: 325–348Google Scholar
  12. INAG (1999) Homepage of the Portuguese Water Institute, Accessed 12 of September 1999 Scholar
  13. Kaufmann A, Gupta M (1985) Introduction to Fuzzy Arithmetic: Theory and Applications. Van Nostrand, NY.Google Scholar
  14. Klir G, Yuan B (1995) Fuzzy Sets and Fuzzy Logic-Theory and Applications. Prentice Hall PTR, New Jersey.Google Scholar
  15. Longley P, Goodchild M, Maguire D, Rhind D (2001) Geographical Information Systems and Science. John Wiley & Sons. New York.Google Scholar
  16. Lowell K (1994) An uncertainty-based spatial representation for natural resources phenomena. Advances in GIS research 2: 933–944Google Scholar
  17. Rump S (1998) INTLAB — INTerval LABoratory. Technical University Hamburg, Germany. (URL Scholar
  18. Zhang J (1996) A Surface Approach to the Handling of Uncertainties in an Integrated Spatial Database Environment. Cartographica 33: 23–31Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Cidália Costa Fonte
    • 1
  • Weldon A. Lodwick
    • 2
  1. 1.Secção de Engenharia Geográfica, Departamento de Matemática da Faculdade de Ciências e Tecnologia da Universidade de CoimbraCoimbraPortugal
  2. 2.Mathematics DepartmentUniversity of Colorado at DenverDenverUSA

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