A fuzzy topology for computing the interior, boundary, and exterior of spatial objects quantitatively in GIS

Computers and Geosciences

Volumn 33, Issue 7, 2007, Pages 898-915

  Shi, Wenzhong ^a   Liu, Kimfung ^a  

^a HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

Author keywords

Closure operator; Interior operator; Topological relations

Indexed keywords

AERIAL PHOTOGRAPHY; COMPUTATIONAL METHODS; FUZZY SETS; MAPPING; MATHEMATICAL OPERATORS; TOPOLOGY;

CLOSURE OPERATOR; FUZZY TOPOLOGY; INTERIOR OPERATOR; SPATIAL OBJECTS; TOPOLOGICAL RELATIONS;

GEOGRAPHIC INFORMATION SYSTEMS;

AERIAL PHOTOGRAPHY; COMPUTATIONAL METHODS; FUZZY SETS; GEOGRAPHIC INFORMATION SYSTEMS; MAPPING; MATHEMATICAL OPERATORS; TOPOLOGY;

AERIAL PHOTOGRAPH; FUZZY MATHEMATICS; GIS; QUANTITATIVE ANALYSIS; TOPOLOGY;

ASIA; CHINA; EURASIA; FAR EAST; HONG KONG;

MIKANIA MICRANTHA;

EID: 34249708295     PISSN: 00983004     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cageo.2006.10.013     Document Type: Article

References (29)

1. Apostol, T.M., 1974. Mathematical Analysis, Addison-Wesley Publishing Company, Inc. 492pp.
2. Blakemore M. Generalisation and error in spatial data bases. Cartographica 21 (1984) 131-139
3. Chang C.L. Fuzzy topological spaces. Journal of Mathematical Analysis and Applications 24 (1968) 182-190
4. Clementini, E., Di Felice, D.P., 1996. An algebraic model for spatial objects with indeterminate boundaries. In: Burrough, P.A., Frank, A.U. (Eds.), Geographic Objects with Indeterminate Boundaries. Taylor & Francis, London, pp. 155-169.
5. Cohn, A.G., Gotts, N.M., 1996. The 'egg-yolk' representation of regions with indeterminate boundaries. In: Burrough, P.A., Frank, A.U. (Eds.), Geographic Objects with Indeterminate Boundaries. Taylor & Francis, London, pp. 171-187.
6. Du, S., Qin, Q., Wang, Q., 2005a. Fuzzy description of topological relations I: a unified fuzzy 9-intersection model. In: Wang, L., Chen, K., Ong, Y.S. (Eds.), Advances in Natural Computation, Lecture Notes in Computer Science, vol. 3612, pp. 1260-1273.
7. Du, S., Qin, Q., Wang, Q., 2005b. Fuzzy description of topological relations II: computation methods and examples. In: Wang, L., Chen, K., Ong, Y.S. (Eds.), Advances in Natural Computation, Lecture Notes in Computer Science, vol. 3612, pp. 1274-1279.
8. Egenhofer M. A model for detailed binary topological relationships. Geomatica 47 3,4 (1993) 261-273
9. Egenhofer M., and Franzosa R. Point-set topological spatial relations. International Journal of Geographical Information Systems 5 2 (1991) 161-174
10. Egenhofer, M., Herring, J., 1991. Categorizing binary topological relations between regions, lines and points in geographic databases. Technical Report, Department of Surveying Engineering, University of Maine, 28pp.
11. Gaal, S.A., 1964. Point Set Topology. Academic Press, New York-London, 317pp.
12. Li C., Chen J., and Li Z. Raster-based method or the generation of Voronoi diagrams for spatial entities. International Journal of Geographical Information Systems 13 3 (1999) 209
13. Liu K.F., and Shi W.Z. Computing the fuzzy topological relations of spatial objects based on induced fuzzy topology. International Journal of Geographical Information Science (IJGIS) 20 8 (2006) 857-883
14. Liu, K.F., Shi, W.Z., Huang, C.Q., 2004. Fuzzy image processing method in GIS. In: Proceedings Greater China GIS Conference 2004, 9th-11th December 2004, Hong Kong.
15. Liu, Y.M., Luo, M.K., 1997. Fuzzy Topology. World Scientific, Singapore, 353pp.
16. Pascali, E., Ajmal, N., 1997. Fuzzy topologies and a type of their decomposition. Rendiconti di Matematica, Serie VII, vol. 17, Roma, pp. 305-328.
17. Shi, W.Z., Guo, W., 1999. Topological relations between uncertainty spatial objects in three-dimensional space. In: Proceedings of International Symposium on Spatial Data Quality, July 1999, Hong Kong. pp. 487-495.
18. Shi, W.Z., Liu, K.F., 2004. Modelling fuzzy topological relations between uncertain objects in GIS. Photogrammetric Engineering and Remote Sensing 70(8), 921-930.
19. Shi, W.Z., Dai, E., Liu, C., 2003. Characteristics of Mikania micrantha on infrared air photo. 47pp. (Unpublished internal technical report).
20. Smith B. Mereotopology: a theory of parts and boundaries. Data & Knowledge Engineering 20 (1996) 287-303
21. Tang, X.M., 2004. Spatial object modelling in fuzzy topological spaces: with applications to land cover change. Ph.D. Dissertation, University of Twente, Netherlands, 218pp.
22. Tang, X.M., Kainz, W., 2002. Analysis of topological relations between fuzzy regions in general fuzzy topological space. In: Proceedings The SDH Conference 02', Ottawa, Canada, pp. 114-123.
23. Tang, X.M., Kainz, W., Yu, F., 2003. Modelling of fuzzy spatial objects and topological relations. In: Proceedings of the Second International Symposium on Spatial Data Quality '03, Hong Kong, pp. 61-71.
24. Tang X.M., Kainz W., and Fang Y. Reasoning about changes of land covers with fuzzy settings. International Journal of Remote Sensing 26 14 (2005) 3025-3046
25. Wang F., Hall G.B., and Subaryono W.F. Fuzzy information representation and processing in conventional GIS software: database design and application. International Journal of Geographical Information Systems 4 3 (1990) 261-283
26. Winter S. Uncertain topological relations between imprecise regions. International Journal of Geographical Information Science 14 5 (2000) 411-430
27. Wong C.K. Fuzzy points and local properties of fuzzy topology. Journal of Mathematical Analysis and Applications 46 (1974) 316-328
28. Wu G., and Zheng C. Fuzzy boundary and characteristic properties of order-homomorphisms. Fuzzy Sets and Systems 39 (1991) 329-337
29. Zadeh L.A. Fuzzy sets. Information and Control 8 (1965) 338-353