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Vague regions

  • Spatial Data Models
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Advances in Spatial Databases (SSD 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1262))

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Abstract

In many geographical applications there is a need to model spatial phenomena not simply by sharp objects but rather through indeterminate or vague concepts. To support such applications we present a model of vague regions which covers and extends previous approaches. The formal framework is based on a general exact model of spatial data types. On the one hand, this simplifies the definition of the vague model since we can build upon already existing theory of spatial data types. On the other hand, this approach facilitates the migration from exact to vague models. Moreover, exact spatial data types are subsumed as a special case of the presented vague concepts. We present examples and show how they are represented within our framework. We give a formal definition of basic operations and predicates which particularly allow a more fine-grained investigation of spatial situations than in the pure exact case. We also demonstrate the integration of the presented concepts into an SQL-like query language.

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References

  1. P. Alexandroff. Elementary Concepts of Topology. Dover Publications, 1961.

    Google Scholar 

  2. D. Altman. Fuzzy Set Theoretic Approaches for Handling Imprecision in Spatial Analysis. Int. Journal of Geographical Information Systems, vol. 8, no. 3, pp. 271–289, 1994.

    Google Scholar 

  3. M.A. Armstrong. Basic Topology. Springer Verlag, 1983.

    Google Scholar 

  4. R. Banai. Fuzziness in Geographical Information Systems: Contributions from the Analytic Hierarchy Process. Int. Journal of Geographical Information Systems, vol. 7, no. 4, pp. 315–329, 1993.

    Google Scholar 

  5. M. Blakemore. Generalization and Error in Spatial Databases. Cartographica, vol. 21, 1984.

    Google Scholar 

  6. PA. Burrough. Natural Objects with Indeterminate Boundaries. Geographic Objects with Indeterminate Boundaries, GISDATA Series, vol. 3, Taylor & Francis, pp. 3–28, 1996.

    Google Scholar 

  7. E. Clementini & P. di Felice. An Algebraic Model for Spatial Objects with Indeterminate Boundaries. Geographic Objects with Indeterminate Boundaries, GISDATA Series, vol. 3, Taylor & Francis, pp. 153–169, 1996.

    Google Scholar 

  8. A.G. Cohn & N.M. Gotts. The ‘Egg-Yolk’ Representation of Regions with Indeterminate Boundaries. Geographic Objects with Indeterminate Boundaries, GISDATA Series, vol. 3, Taylor & Francis, pp. 171–187, 1996.

    Google Scholar 

  9. H. Couclelis. Towards an Operational Typology of Geographic Entities with Ill-defined Boundaries. Geographic Objects with Indeterminate Boundaries, GISDATA Series, vol. 3, Taylor & Francis, pp. 45–55, 1996.

    Google Scholar 

  10. M.J. Egenhofer, E. Clementini & P. di Felice. Topological Relations between Regions with Holes. Int. Journal of Geographical Information Systems, vol. 8, no. 2, pp. 129–142, 1994.

    Google Scholar 

  11. G. Edwards. Characterizing and Maintaining Polygons with Fuzzy Boundaries in GIS. 6th Int. Symp. on Spatial Data Handling, pp. 223–239, 1994.

    Google Scholar 

  12. M.J. Egenhofer. Spatial SQL: A Spatial Query Language. Report 103, Dept. of Surveying Engineering, University of Maine, 1989.

    Google Scholar 

  13. M. Erwig & R.H. Güting. Explicit Graphs in a Functional Model for Spatial Databases. IEEE Transactions on Knowledge and Data Engineering, vol. 6, no. 5, pp. 787–804, 1994.

    Google Scholar 

  14. M. Erwig. Graphs in Spatial Databases. Doctoral Thesis, Fern Universität Hagen, 1994.

    Google Scholar 

  15. J.T. Finn. Use of the Average Mutual Information Index in Evaluating Classification Error and Consistency. Int. Journal of Geographical Information Systems, vol. 7, no. 4, pp. 349–366, 1993.

    Google Scholar 

  16. S. Gaal. Point Set Topology. Academic Press, 1964.

    Google Scholar 

  17. R.H. Güting & M. Schneider. Realms: A Foundation for Spatial Data Types in Database Systems. 3rd Int. Symp. on Large Spatial Databases, pp. 14–35, 1993.

    Google Scholar 

  18. R.H. Güting & M. Schneider. Realm-Based Spatial Data Types: The ROSE Algebra. VLDB Journal, vol. 4, pp. 100–143, 1995.

    Google Scholar 

  19. R.H. Güting. Geo-Relational Algebra: A Model and Query Language for Geometric Database Systems. Int. Conf. on Extending Database Technology, pp. 506–527, 1988.

    Google Scholar 

  20. V.J. Kollias & A. Voliotis. Fuzzy Reasoning in the Development of Geographical Information Systems. Int. Journal of Geographical Information Systems, vol. 5, no. 2, pp. 209–223, 1991.

    Google Scholar 

  21. P. Lagacherie, P. Andrieux & R. Bouzigues. Fuzziness and Uncertainty of Soil Boundaries: From Reality to Coding in GIS. Geographic Objects with Indeterminate Boundaries, GISDATA Series, vol. 3, Taylor & Francis, pp. 275–286, 1996.

    Google Scholar 

  22. U. Lipeck & K. Neumann. Modelling and Manipulating Objects in Geoscientinc Databases. 5th Int. Conf. on the Entity-Relationship Approach, pp. 67–86, 1987.

    Google Scholar 

  23. M. Schneider. Spatial Data Types for Database Systems. Doctoral Thesis, Fern Universität Hagen, 1995.

    Google Scholar 

  24. M. Schneider. Modelling Spatial Objects with Undetermined Boundaries Using the Realm/ROSE Approach. Geographic Objects with Indeterminate Boundaries, GISDATA Series, vol. 3, Taylor & Francis, pp. 141–152, 1996.

    Google Scholar 

  25. R. Shibasaki. A Framework for Handling Geometric Data with Positional Uncertainty in a GIS Environment. GIS: Technology and Applications, World Scientific, pp. 21–35, 1993.

    Google Scholar 

  26. M. Scholl & A. Voisard. Thematic Map Modeling. 1st Int. Symp. on Large Spatial Databases, pp. 167–190, 1989.

    Google Scholar 

  27. R.B. Tilove. Set Membership Classification: A Unified Approach to Geometric Intersection Problems. IEEE Transactions on Computers, vol. C-29, pp. 874–883, 1980.

    Google Scholar 

  28. E. L. Usery. A Conceptual Framework and Fuzzy Set Implementation for Geographic Features. Geographic Objects with Indeterminate Boundaries, GISDATA Series, vol. 3, Taylor & Francis, pp. 71–85, 1996.

    Google Scholar 

  29. F. Wang. Towards a Natural Language User Interface: An Approach of Fuzzy Query. Int. Journal of Geographical Information Systems, vol. 8, no. 2, pp. 143–162, 1994.

    Google Scholar 

  30. M.F. Worboys & P. Bofakos. A Canonical Model for a Class of Areal Spatial Objects. 3rd Int. Symp. on Advances in Spatial Databases, Springer-Verlag, LNCS 692, pp. 36–52, 1993.

    Google Scholar 

  31. F. Wang & G.B. Hall. Fuzzy Representation of Geographical Boundaries in GIS. Int. Journal of Geographical Information Systems, vol. 10, no. 5, pp. 573–590, 1996.

    Google Scholar 

  32. F. Wang, G.B. Hall & Subaryono. Fuzzy Information Representation and Processing in Conventional GIS Software: Database Design and Application. Int. Journal of Geographical Information Systems, vol. 8, no. 2, pp. 143–162, 1994.

    Google Scholar 

  33. L.A. Zadeh. Fuzzy Sets. Information and Control, vol. 8, pp. 338–353, 1965.

    Google Scholar 

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Michel Scholl Agnès Voisard

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© 1997 Springer-Verlag Berlin Heidelberg

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Erwig, M., Schneider, M. (1997). Vague regions. In: Scholl, M., Voisard, A. (eds) Advances in Spatial Databases. SSD 1997. Lecture Notes in Computer Science, vol 1262. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63238-7_36

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  • DOI: https://doi.org/10.1007/3-540-63238-7_36

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63238-2

  • Online ISBN: 978-3-540-69240-9

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