Advertisement

Implementable Representations of Level-2 Fuzzy Regions for Use in Databases and GIS

  • Jörg Verstraete
Part of the Communications in Computer and Information Science book series (CCIS, volume 297)

Abstract

Many spatial data are prone to uncertainty and imprecision, which calls for a way of representing such information. In this contribution, implementable models for the representation of level-2 fuzzy regions are presented. These models are designed to still adhere to the theoretical model of level-2 fuzzy regions - which employs fuzzy set theory and uses level-2 fuzzy sets to combine imprecision with uncertainty - but impose some limitations and modifications so that they can be represented and used in a computer system. These limitations are mainly aimed at restricting the amount of data that needs to be stored; apart from the representation structures, the operations also need to be defined in an algorithmic and computable way.

Keywords

Membership Function Candidate Region Membership Grade Fuzzy Region Constrain Delaunay Triangulation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Clementini, E.: Modelling spatial objects affected by uncertainty. In: De Caluwe, R., De Tré, G., Bordogna, G. (eds.) Spatio-Temporal Databases - Flexible Querying and Reasoning, pp. 211–236. Springer (2004)Google Scholar
  2. 2.
    Cohn, A., Gotts, N.M.: Spatial regions with undetermined boundaries. In: Proceedings of the Second ACM Workshop on Advances in GIS, pp. 52–59 (1994)Google Scholar
  3. 3.
    Du, S., Qin, Q., Wang, Q., LI, B.: Fuzzy Description of Topological Relations I: A Unified Fuzzy 9-Intersection Model. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005, Part III. LNCS, vol. 3612, pp. 1261–1273. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Bloch, I.: Spatial reasoning under imprecision using fuzzy set theory, formal logics and mathematical morphology. International Journal of Approximate Reasoning 41(2), 77–95 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Kanjilal, V., Liu, H., Schneider, M.: Plateau Regions: An Implementation Concept for Fuzzy Regions in Spatial Databases and GIS. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS, vol. 6178, pp. 624–633. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Rigaux, P., Scholl, M., Voisard, A.: Spatial databases with applications to GIS. Morgan Kaufman Publishers (2002)Google Scholar
  7. 7.
    Schneider, M., Pauly, A.: ROSA: An Algebra for Rough Spatial Objects in Databases. In: Yao, J., Lingras, P., Wu, W.-Z., Szczuka, M.S., Cercone, N.J., Ślęzak, D. (eds.) RSKT 2007. LNCS (LNAI), vol. 4481, pp. 411–418. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Shewchuk, J.R.: Triangle: Engineering a 2d quality mesh generator and delaunay triangulator. In: First Workshop on Applied Computational Geometry, Philadelphia, Pennsylvania, pp. 124–133. Association for Computing Machinery (1996)Google Scholar
  9. 9.
    Somodevilla, M.J., Petry, F.E.: Fuzzy minimum bounding rectangles; in spatio-temporal databases - flexible querying and reasoning. In: De Caluwe, R., De Tré, G., Bordogna, G. (eds.) Spatio-Temporal Databases - Flexible Querying and Reasoning, pp. 237–263. Springer (2004)Google Scholar
  10. 10.
    Verstraete, J.: Fuzzy Regions: interpretations of surface area and distance. Control and Cybernetics 38, 509–526 (2009)MathSciNetGoogle Scholar
  11. 11.
    Verstraete, J., De Tré, G., De Caluwe, R., Hallez, A.: Field based methods for the modelling of fuzzy spatial data. In: Fred, P., Vince, R., Maria, C. (eds.) Fuzzy Modeling with Spatial Information for Geographic Problems, pp. 41–69. Springer (2005)Google Scholar
  12. 12.
    Verstraete, J., De Tré, G., Hallez, A., De Caluwe, R.: Using tin-based structures for the modelling of fuzzy gis objects in a database. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15, 1–20 (2007)CrossRefGoogle Scholar
  13. 13.
    Verstraete, J., Hallez, A., De Tré, G.: Bitmap Based Structures for the modelling of Fuzzy Entities. Control & Cybernetics 35(1), 147–164 (2006)zbMATHGoogle Scholar
  14. 14.
    Verstraete, J., Hallez, A., Guy, De Tré, G., Tom, M.: Topological relations on fuzzy regions: an extended application of intersection matrices. In: Bouchon-Meunier, B., Yager, R.R., Marsala, C., Rifqi, M. (eds.) Uncertainty and Intelligent Information Systems, pp. 487–500. World Scientific (2008)Google Scholar
  15. 15.
    Verstraete, J., Van der Cruyssen, B., De Caluwe, R.: Assigning membership degrees to points of fuzzy boundaries. In: NAFIPS 2000 Conference Proceedings, Atlanta, USA. NAFIPS, pp. 444–447 (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jörg Verstraete
    • 1
    • 2
  1. 1.Instytut Badań SystemowychPolskiej Akademii Nauk (Systems Research Institute, Polish Academy of Sciences)WarszawaPoland
  2. 2.DDCM, Dept. Telecommunications and Information ProcessingGhent UniversityGhentBelgium

Personalised recommendations