Abstract
In many geographical applications there is a need to model spatial phenomena not simply by sharply bounded objects but rather through vague concepts due to indeterminate boundaries. Spatial database systems and geographical information systems are currently not able to deal with this kind of data. In order to support these applications, for an important kind of vagueness called fuzziness, we propose an abstract, conceptual model of so-called fuzzy spatial data types (i.e., a fuzzy spatial algebra) introducing fuzzy points, fuzzy lines, and fuzzy regions. This paper* focuses on defining their structure and semantics. The formal framework is based on fuzzy set theory and fuzzy topology.
This research was partially supported by the CHOROCHRONOS project, funded by the EU under the Training and Mobility of Researchers Programme, contract no. ERB FMRX-CT96-0056.
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References
D. Altman. Fuzzy Set Theoretic Approaches for Handling Imprecision in Spatial Analysis. Int. Journal of Geographical Information Systems, 8(3):271–289, 1994.
P.A. Burrough and A.U. Frank, editors. Geographic Objects with Indeterminate Boundaries, volume 2 of GISDATA Series. Taylor & Francis, 1996.
M. Blakemore. Generalization and Error in Spatial Databases. Cartographica, 21, 1984.
P.A. Burrough. Natural Objects with Indeterminate Boundaries. In [BF9], pages 3–28, 1996.
E. Clementini and P. di Felice. An Algebraic Model for Spatial Objects with Indeterminate Boundaries. In [BF96], pages 153–169, 1996.
A.G. Cohn and N.M. Gotts. The ‘Egg-Yolk’ Representation of Regions with Indeterminate Boundaries. In [BF96], pages 171–187, 1996.
C.L. Chang. Fuzzy Topological Spaces. Journal of Mathematical Analysis and Applications, 24:182–190, 1968.
S. Dutta. Qualitative Spatial Reasoning: A Semi-Quantitative Approach Using Fuzzy Logic. 1st Int. Symp. on the Design and Implementation of Large Spatial Databases (SSD’89), Springer-Verlag, LNCS 409:345–364, 1989.
S. Dutta. Topological Constraints: A Representational Framework for Approximate Spatial and Temporal Reasoning. 2nd Int. Symp. on Advances in Spatial Databases (SSD’91), Springer-Verlag, LNCS 525:161–180, 1991.
M.J. Egenhofer, E. Clementini, and P. di Felice. Topological Relations between Regions with Holes. Int. Journal of Geographical Information Systems, 8(2):128–142, 1994.
M. Erwig and M. Schneider. Partition and Conquer. 3rd Int. Conf. on Spatial Information Theory (COSIT’97), Springer-Verlag, LNCS 1329:389–408, 1997.
M. Erwig and M. Schneider. Vague Regions. 5th Int. Symp. on Advances in Spatial Databases (SSD’97), Springer-Verlag, LNCS 1262:298–320, 1997.
J.T. Finn. Use of the Average Mutual Information Index in Evaluating Classification Error and Consistency. Int. Journal of Geographical Information Systems, 7(4):349–366, 1993.
S. Gaal. Point Set Topology. Academic Press, 1964.
R.H. Güting and M. Schneider. Realm-Based Spatial Data Types: The ROSE Algebra. VLDB Journal, 4:100–143, 1995.
V.J. Kollias and A. Voliotis. Fuzzy Reasoning in the Development of Geographical Information Systems. Int. Journal of Geographical Information Systems, 5(2):209–223, 1991.
P. Lagacherie, P. Andrieux, and R. Bouzigues. Fuzziness and Uncertainty of Soil Boundaries: From Reality to Coding in GIS. In [BF96], pages 275–286, 1996.
F.P. Preparata and M.I. Shamos. Computational Geometry. Springer Verlag, 1985.
M. Schneider. Modelling Spatial Objects with Undetermined Boundaries Using the Realm/ROSE Approach. In [BF96], pages 141–152, 1996.
M. Schneider. Spatial Data Types for Database Systems-Finite Resolution Geometry for Geographic Information Systems, volume LNCS 1288. Springer-Verlag, Berlin Heidelberg, 1997.
R. Shibasaki. A Framework for Handling Geometric Data with Positional Uncertainty in a GIS Environment. GIS: Technology and Applications, pages 21–35, World Scientific, 1993.
R.B. Tilove. Set Membership Classification: A Unified Approach to Geometric Intersection Problems. IEEE Transactions on Computers, C-29:874–883, 1980.
E.L. Usery. A Conceptual Framework and Fuzzy Set Implementation for Geographic Features. In [BF96], pages 71–85, 1996.
F. Wang. Towards a Natural Language User Interface: An Approach of Fuzzy Query. Int. Journal of Geographical Information Systems, 8(2):143–162, 1994.
M.F. Worboys and P. Bofakos. A Canonical Model for a Class of Areal Spatial Objects. 3rd Int. Symp. on Advances in Spatial Databases (SSD’93), Springer-Verlag, LNCS 692:36–52, 1993.
F. Wang, G.B. Hall, and Subaryono. Fuzzy Information Representation and Processing in Conventional GIS Software: Database Design and Application. Int. Journal of Geographical Information Systems, 4(3):261–283, 1990.
L.A. Zadeh. Fuzzy Sets. Information and Control, 8:338–353, 1965.
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Schneider, M. (1999). Uncertainty Management for Spatial Datain Databases: Fuzzy Spatial Data Types. In: Güting, R.H., Papadias, D., Lochovsky, F. (eds) Advances in Spatial Databases. SSD 1999. Lecture Notes in Computer Science, vol 1651. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48482-5_20
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DOI: https://doi.org/10.1007/3-540-48482-5_20
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