Field Based Methods for the Modeling of Fuzzy Spatial Data

  • Jörg Verstraete
  • Guy De Tré
  • Rita De Caluwe
  • Axel Hallez


In this chapter, two different field based techniques for the modeling of fuzzy information spread over a geographic region, are presented and are compared regarding their applicability. The first one is a vector-mode approach, using triangulated irregular networks (or TINs), the second one is a raster (bitmapmode) approach. Appropriate aggregation operators are defined in both approaches and illustrated by means of examples. The feasibility of the implementation of the operators (by approximation whenever required) is studied. Attention has been paid to the applicability, advantages and disadvantages of both methods in flexible querying.


Membership Function Fuzzy Number Triangular Fuzzy Number Membership Grade Possibility Distribution 
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. Clementini E, Di Felice P (1994) An algebraic model for spatial objects with undetermined boundaries. GISDATA Specialist Meeting-revised version.Google Scholar
  2. Cobb M, Foley H., Petry F and Shaw K (2000). Uncertainty in the Distributed and Interoperable Spatial Information Systems. In: Recent Issues on Fuzzy Databases (eds. G. Bordogna, G. Pasi); Physica-Verlag, Heidelberg, GR, pp 85–108.Google Scholar
  3. Cohn AG, Gotts NM (1994); Spatial regions with undetermined boundaries. In: Proceedings of the Second ACM Workshop on Advances in Geographic Information Systems, pp 52–59.Google Scholar
  4. de Cooman, G (1995) Towards a possiblistic logic. In: Fuzzy set theory and advanced mathematical applications (ed. Ruan D.) Kluwer Academic publishers, Boston, pp 89–133.Google Scholar
  5. de Cooman, G (1999) From possibilistic information to Kleene’s strong multivalued logics. In: Fuzzy sets, logics and reasoning about knowledge (ed. Dubois D.) Kluwer Academic publishers, Boston, pp 315–323.Google Scholar
  6. De Tré G, De Caluwe R, Hallez A, Verstraete J (2002) Fuzzy and Uncertain Spatio-Temporal Database Models: A Constraint-Based Approach. In: Proceedings of the 9th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2002, July 1–5, Annecy, France, pp. 1713–1720.Google Scholar
  7. De Tré G (2002) Extended Possibilistic Truth Values. In: International Journal of Intelligent Systems, volume 17, no. 4, April 2002, Wiley Publishers, pp. 427–446.Google Scholar
  8. De Tré G, Hallez A, Verstraete J, Verkeyn A (2002b), Beyond Conjucative Aggregation of Possibilistic Truth Values in Database Systems. In: The Seventh Meeting of the EURO Working Group on Fuzzy Sets — Eurofuse, pp 137–142.Google Scholar
  9. Dubois D, Prade H (1997) The three semantics of fuzzy sets. In: Fuzzy Sets and Systems, volume 90, Elsevier Science, pp 141–150.Google Scholar
  10. Dubois D, Prade H (2000) Fundamentals of Fuzzy Sets. Kluwer Academic Publishers.Google Scholar
  11. Dubois D, Prade H (2001); Possibility theory, probability theory and multiple-valued logics: A clarification. In: Annals of Mathematics and Artificial Intelligence, volume 32, pp 35–66.CrossRefGoogle Scholar
  12. Gotts NM, Cohn AG (1995) A mereological approach to representing spatial vagueness, Working Papers, Ninth International Workshop on Qualitative Reasoning; pp 246–255.Google Scholar
  13. Hallez A, Verstraete J, De Tré G, De Caluwe R (2002) Contourline Based Modelling of Vague Regions. In: Proceedings of the 9th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems IPMU 2002, July 1–5, Annecy, France.Google Scholar
  14. Klir GJ, Yuan B (1995) Fuzzy sets and fuzzy logic: Theory and applications. New Jersey, Prentice Hall.Google Scholar
  15. Mendel JM (2001) Uncertain Rule-Based Fuzzy Logic Systems, Introduction and New Directions. Prenctice Hall PTR.Google Scholar
  16. Morris A (2001) Why Spatial Databases Need Fuzziness, In: Proceedings of Nafips 2001, pp 2446–2451.Google Scholar
  17. Prade H (1982) Possibility sets, fuzzy sets and their relation to Lukasiewicz logic. In: Proceedings of the 12th International Symposium on Multiple-Valued Logic, pp 223–227.Google Scholar
  18. Rigaux P, Scholl M, Voisard A (2002) Spatial Databases with Applications to GIS. Morgan-Kaufman Publishers.Google Scholar
  19. Schneider M (1999) Uncertainty management for spatial data in databases: fuzzy spatial data types. In: 6th International Symposium on Advances in Spatial Databases (SSD), LNCS 1651, Springer Verlag; pp 330–351.Google Scholar
  20. Shekhar S, Chawla S (2003) Spatial Databases: A tour. Pearson Education Inc.Google Scholar
  21. Shewchuk JR (1996) Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. In: First Workshop on Applied Computational Geometry (Philadelphia, Pennsylvania), Association for Computing Machinery, pp 124–133.Google Scholar
  22. Shewchuk JR (2002) Constrained Delaunay Tetrahedralizations and Provably Good Boundary Recovery; Submitted to the Eleventh International Meshing Roundtable.Google Scholar
  23. Kerre E, Van Schooten A (1988) A Deeper Look on Fuzzy Numbers from a Theoretical as well as from a Practical Point of View. In: Fuzzy Logic in Knowledge-Based Systems, Decision and Control (eds. Gupta M. & Yamakawa T.), Elsevier Science Publishers B.V., North-Holland, pp 173–196.Google Scholar
  24. Vertraete J, Van Der Cruyssen B, De Caluwe R (2000) Assigning Membership Degrees to Points of Fuzzy Boundaries. In: Proceedings of the 19th International Conference of the North American Fuzzy Information Processing Society-Nafips, pp 444–447.Google Scholar
  25. Verstraete J, De Tré G, Hallez A (2002), Adapting TIN-layers to Represent Fuzzy Geographic Information. In: The Seventh Meeting of the EURO Working Group on Fuzzy Sets — Eurofuse, pp 57–62.Google Scholar
  26. Zimmerman H-J (1999), Practical Applications of Fuzzy Technologies, Kluwer Academic Publishers.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jörg Verstraete
    • 1
  • Guy De Tré
    • 1
  • Rita De Caluwe
    • 1
  • Axel Hallez
    • 1
  1. 1.Department of Telecommunications and Information ProcessingGhent UniversityGhentBelgium

Personalised recommendations