Abstract
Gradation, the presence of gradual rather than abrupt boundaries around geographic entities, is one of the many complexities of geography which is beginning to be investigated for representation and analysis informal models. Much of the research to date has been focused on specific applications, but some are starting to look at the underlying theory behind this phenomenon, leading toward better understanding and better models. This work extends this theory with a taxonomy which describes and explains gradational situations, focusing on issues related to formal representation. This taxonomy has been beneficial in developing methods of representing this phenomenon in GIS and maps.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Altman, D. (1994) Fuzzy set theoretic approaches for handling imprecision in spatial analysis, Int. J. Geographical Information Systems, V.8#3, pp.271–289.
Burrough, P. (1989) Fuzzy mathematical methods for soil survey and land evaluation, J. Soil Science, V.40, pp. 477–492.
Burrough, P., Frank, A.U., eds. (1996) Geographic Objects with Indeterminate Boundaries. London: Taylor & Francis.
Couclelis, H. (1996) Towards an Operational Typology of Geographic Entities with Ill-defined Boundaries, Chapter 3 in Burrough & Frank 1996.
Fisher, P. (1996) Boolean and Fuzzy Regions, Chapter 6 in Burrough & Frank 1996, pp. 87–94.
Freksa, C., Barkowsky, T. (1996) On the Relations between Spatial Concepts and Geographic Objects, Chapter 8 in Burrough & Frank 1996, pp. 129–141.
Gale, S. (1976) A Resolution of the Regionalization Problem and its Implications for Political Geography and Social Justice, Geografiska Annaler, V.58-B#1, pp. 1–16.
Gale, S. (1972) Inexactness, Fuzzy Sets, and the Foundation of Behavioral Geography, Geographical Analysis V.4#4 (Oct), 337–349.
Goguen, J.A. (1968) The Logic of Inexact Concepts, Synthese, V.19, pp.325–373.
Grigg, D. (1967) Regions, Models, and Classes, Chapter 12 in Models in Geography (Chorley, R.J., Haggett, P., eds.), pp. 461–507. London: Methuen.
Kearney, T.H., Peebles, R.H. (1951) Arizona Flora. Berkeley: University of California Press.
Kimble, G.H.T. (1951) The inadequacy of the regional concept, London Essays in Geography (Stamp, L.D., Wooldridge, S.W., eds), pp. 151–174.
Labov, W. (1973) The boundaries of words and their meanings, New Ways of Analyzing Variation in English, Fishman, J., ed., pp. 340–373. Washington, DC: Georgetown University Press.
Lagacherie, P., Andrieux, P., Bouzigues, R (1996) Fuzziness and Uncertainty of Soil Boundaries: From Reality to Coding in GIS, Chapter 18 in Burrough & Frank 1996, pp. 275–286.
Lakoff, G. (1987) Women, Fire, and Dangerous Things: What Categories Reveal About the Mind. Chigago: University of Chicago Press.
Leung, Y (1988) Spatial Analysis and Planning under Imprecision (Studies in Regional Science and Urban Economics Volume 17). Amsterdam: North-Holland. 375 pp.
Leung, Y. (1987) On the imprecision of boundaries, Geographical Analysis, V.19#2 (Apr), pp. 125–151.
Plewe, B. (1997a) The Representation of Gradation in Geographic Information Systems (unpublished Ph.D. dissertation). Buffalo, New York: State University of New York.
Plewe, B. (1997b) The Cartographic Representation of Gradation: Fuzzy Maps from Fuzzy Data, Proc. 1997 ACSM/ASPRS Convention. Falls Church, VA: ACSM.
Poulter, M.A. (1996) On the Integration of Earth Observation Data: Defining Landscape Boundaries to a GIS, Chapter 19 in Burrough & Frank 1996, pp. 287–298.
Robinson, V.B., Frank, A.U. (1985) About different kinds of uncertainty in collections of spatial data, Proc. Auto-Carlo 7, pp. 440–449. Falls Church, VA: ACSM.
Rosch, E. (1978) Principles of categorization, Cognition and Categorization (E. Rosch, B.B. Lloyd, eds.), pp. 27–48. Hillsdale, NJ: Erlbaum.
Smith, B.A. (1995) On Drawing Lines on a Map, Spatial Information Theory: A Theoretical Basis for GIS (Proceedings of COSIT '95), Lecture Notes in Computer Sciences No. 988 (Frank, A.U., Kuhn, W., eds.). Berlin: Springer-Verlag, pp. 475–484.
Soja, E. (1971) The Political Organization of Space, AAG Commission on College Geography Resource Paper #8. Washington, D.C.: Association of American Geographers. 54pp.
Wang, F., Hall, G.B. (1996) Fuzzy representation of geographical boundaries in GIS, Int. J. Geographical Information Systems, V.10#5, pp. 573–590.
Wang, F., Hall, G., Subaryono (1990) Fuzzy information representation and processing in conventional GIS software: database design and application, Int. J. Geographical Information Systems, V.4#3, pp.261–283.
Weinreich, U. (1954) Is a structural dialectology possible? Word, V.10, pp.388–400.
Wittgenstein, L. (1953) Philosophical Investigations. New York: Macmillan.
Zadeh, L.A. (1975) The Concept of a Linguistic Variable and its Application to Approximate Reasoning I, Information Sciences, V.8, pp. 199–249.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Plewe, B. (1997). A representation-oriented taxonomy of gradation. In: Hirtle, S.C., Frank, A.U. (eds) Spatial Information Theory A Theoretical Basis for GIS. COSIT 1997. Lecture Notes in Computer Science, vol 1329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63623-4_46
Download citation
DOI: https://doi.org/10.1007/3-540-63623-4_46
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63623-6
Online ISBN: 978-3-540-69616-2
eBook Packages: Springer Book Archive