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Deriving topological concepts for fuzzy regions: from properties to definitions

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Języki publikacji
EN
Abstrakty
EN
Fuzzy regions are a concept allowing the uncertain or imprecise spatial data to be represented. Many geographic or spatial data are prone to uncertainty or imprecision and while such data can be represented, it is still necessary to be able to perform basic tasks one expects to perform in a geographic context. A number of operations have been considered in the past; in this contribution the topological concepts of fuzzy regions will be examined. For this purpose, appropriate definitions for the boundary, interior and exterior of fuzzy regions will be developed. These definitions can then be applied in an extension of the 9-intersection model.
Rocznik
Strony
113--143
Opis fizyczny
Bibliogr. 32 poz., il., wykr.
Twórcy
Bibliografia
  • Beaubouef, T. and Petry, F. (2001) Vagueness in spatial data: Rough set and egg-yolk approaches. In: Proceedings of IEA/AIE 2001 Conference (Budapest, Hungary, 2001). LNEIS 2007, Springer-Verlag, 367-373.
  • Beaubouef, T. and Petry, F. (2007) Spatial data methods and vague regions: A rough set approach. Applied Soft Computing 7,1, 425-440.
  • Bejaoui, L., Pinet, F., Bedard, Y. and Schneider, M. (2008) Qualified topological relations between spatial objects with possible vague shape. International Journal of Geographical Information Science, 1-45.
  • Clementini, E. (2004) Modelling spatial objects affected by uncertainty. In: R. De Caluwe, G. De Tré, and G. Bordogna, eds., Spatio-Temporal Data-bases - Flexible Querying and Reasoning, Springer-Verlag, 211-236.
  • Clementini, E. and Di Felice, P. (1996) An algebraic model for spatial objects with undetermined boundaries. In: P.A. Burrough, ed., Geographic Objects with Indeterminate Boundaries. Taylor & Francis, 155-169.
  • Cohn,A. and Gotts,N.M. (1994) Spatial regions with undetermined boundaries. In: Proceedings of the Gaithesburg Workshop on GIS. ACM, 52-59.
  • Du, S., Qin, Q. and Wang, Q. (2008) Reasoning about topological relations between regions with broad boundaries. International Journal of Approximate Reasoning 47,2, 219-232.
  • Du, S., Qin, Q., Wang, Q. and Li, B. (2005a) Fuzzy description of topological relations i: a unified fuzzy 9-intersection model. In: W. Wang, K. Chen, and Y. Soon Ong, eds., Advances in Natural Computation. LNCS 3612, Springer Verlag, 1261-1273.
  • Du, S., Qin, Q., Wang, Q. and Li, B. (2005b) Fuzzy description of topological relations ii: Computation methods and examples. In: W. Wang, K. Chen, and Y. Soon Ong, eds., Advances in Natural Computation, LNCS 3612, 1274- 1279.
  • Dubois, D. and Prade, H. (1999) The three semantics of fuzzy sets. Fuzzy Sets and Systems, 90, 141-150.
  • Dubois, D. and Prade, H. (2000) Fundamentals of Fuzzy Sets. Kluwer Academic Publishers.
  • Egenhofer, M. and Sharma, J. (1993) Topological relations between regions in r2 and z2. In: D. Abel and Ooi B.Ch., eds., Advances in Spatial Databases - Third International Symposium SSD’93. LNCS 692, Springer Verlag, 316-336.
  • Gotts, N.M. and Cohn, A.G. (1996) A mereological approach to representing spatial vagueness. In: Principles of Knowledge Representation and Reasoning. Proc of the 5th Conference, 246-255.
  • Gottwald, S. (1979) Set theory for fuzzy sets of higher level. Fuzzy Sets and Systems 2, 2 , 125-151.
  • Klir, G.J. and Yuan, B. (1995) Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, New Jersey.
  • Mendel, J.M. (2001) Uncertain Rule-Based Fuzzy Logic Systems. Introduction and New Directions. Prentice Hall.
  • Petry, F.E., Robinson, V.B. and Cobb, M.A. (2005) Fuzzy Modeling with Spatial Information for Geographic Problems. Springer-Verlag.
  • Schneider, M. (1996) Geographic Objects with Indeterminate Boundaries, GISDATA Series, 2. Taylor & Francis, 141-152.
  • Schneider, M. and Pauly, A. (2007) Rosa: An algebra for rough spatial objects in databases. In: 2nd International Conference on Rough Sets and Knowledge Technology (RSKT). LNAI 4481, Springer-Verlag, 411-418.
  • Schockaert, S., De Cock,M. and Cornelis,C. (2008) Fuzzy region connection calculus: Representing vague topological information. International Journal of Approximate Reasoning, 48,1, 314-331.
  • Verstraete, J. (2010a) Fuzzy regions: adding subregions and the impast on surface and distance calculation. In: E. Hüllermeier, R. Kruse and F. Hoffmann, eds., Information Processing and Management of Uncertainty in Knowledge-Based Systems - Theory and Methods, 13th International Conference on Information Processing and Management of Uncertainty, IPMU 2010, Communications in Computer and Information Science, 80/1, Springer, 561-570.
  • Verstraete, J. (2010b) A quantitative approach to topology for fuzzy regions. In: Artificial Intelligence and Soft Computing, LNCS 6113, Springer, 248-255.
  • Verstraete, J. (2011a) Using level-2 fuzzy sets to combine uncertainty and imprecision in fuzzy regions. In: E. Mugellini, et al., eds., Advances in Intelligent Web Mastering - 3, Proceedings of the 7th Atlantic Web Intelligence Conference, AWIC 2011, Advances in Intelligent and Soft Computing, 86. Springer-Verlag, 163-172.
  • Verstraete, J. (2011b) Union and intersection of level-2 fuzzy regions. In: World Conference on Soft Computing (accepted for publication).
  • Verstraete, J. (2012) Surface area of level-2 fuzzy regions. In: L. Rutkowski et al., eds., Artificial Inteligence & Soft Computing - 11th International Conference, ICA-ISC 2012. LNCS 2012, 342 - 349.
  • Verstraete, J., De Tré,G., De Caluwe,R. and Hallez, A. (2004) Field Based Methods for the Modeling of Fuzzy Spatial Data. In: M. Cobb, F. Petry and V. Robinson, eds., Fuzzy Modeling with Spatial Information for Geographic Problems. Springer Verlag, 41-69.
  • Verstraete, J., De Tré, G. and Hallez, A. (2002) Adapting Tin-layers to represent fuzzy geographic information. In: The Seventh Meeting of the EURO Working Group on Fuzzy Sets, EUROFUSE, 57-62.
  • Verstraete, J., De Tré,G., Hallez,A. and De Caluwe,R. (2007) 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.
  • Verstraete, J., Hallez, A. and De Tré, G. (2006) Bitmap based structures for the modelling of fuzzy entities. Control & Cybernetics 35,1, 147-164.
  • Verstraete, J., Hallez, A., De Tré, G. and Tom, M. (2008) Topological relations on fuzzy regions: an extended application of intersection matrices. In: B. Bouchon-Meunier, R. R. Yager, C. Marsala, and M. Rifqi, eds., Uncertainty and Intelligent Information Systems, World Scientific, 487-500.
  • Verstraete, J., Van der Cruyssen, B. and De Caluwe, R. (2000) Assigning membership degrees to points of fuzzy boundaries. In: NAFIPS’2000 Conference Proceedings, NAFIPS, 444-447.
  • Winter, S. (2000) Uncertain topological relations between imprecise regions. International Journal of Geographical Informations Science, 14,5, 411-430.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BATC-0009-0040
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