Abstract
The article presents a conceptual framework for computations with imprecise values. Typically, the treatment of imprecise values differs from the treatment of precise values. While precise computations use a single number to characterize a value, computations with imprecise values must deal with several numbers for each value. This results in significant changes in the program code because values are represented, e.g., by expectation and standard deviation and both values must be considered within the computations. It would be desirable to have a solution where only limited changes in very specific places of the code are necessary. The mathematical concept of lifting may lead to such a solution.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bachmann, A. and Allgöwer, B. (2002). Uncertainty Propagation in Wildland Fire and Behaviour Modelling. International Journal of Geographic Information Science 16(2): 115-127.
Bird, R. (1998). Introduction to Functional Programming Using Haskell. Hemel Hempstead, UK, Prentice Hall Europe.
Erwig, M. and Schneider, M. (1999). Developments in Spatio-Temporal Query Languages. Proceedings of 10th International Workshop on Database and Expert Systems Applications, Florence, Italy.
Fodor, J. and Bede, B. (2006). Arithmetics with Fuzzy Numbers: A Comparative Overview. Proceeding of 4th Slovakian-Hungarian Joint Symposium on Applied Machine Intelligence, Herl’any, Slovakia.
Frank, A.U. (2005). Map Algebra Extended with Functors for Temporal Data. Proceedings of the ER Workshop 2005 (CoMoGIS’05). J. Akoka et al. Klagenfurt, Austria, Springer-Verlag Berlin Heidelberg. LNCS 3770: 193-206.
Hayes, B. (2003). A Lucid Interval. American Scientist 91(6): 484-488.
Heuvelink, G.B.M. (1998). Error Propagation in Environmental Modelling with GIS. London, Taylor & Francis.
Heuvelink, G.B.M. and Burrough, P.A. (2002). Developments in Statistical Approaches to Uncertainty and its Propagation. International Journal of Geographic Information Science 16(2): 111-113.
Karssenberg, D. and de Jong, K. (2005). Dynamic Environmental Modelling in GIS: 2. Modelling Error Propagation. International Journal of Geographic Information Science 19(6): 623-637.
MacLane, S. and Birkhoff, G. (1999). Algebra (3rd Edition), AMS Chelsea Publishing.
Marquis, J.-P. (2006). Category Theory, Stanford Encyclopedia of Philosophy.
Moggi, E. (1989). A Category-Theoretic Account of Program Modules. Category Theory and Computer Science, Springer-Verlag, Berlin.
Navratil, G. (2006). Error Propagation for Free? GIScience, Münster, Germany, Institute for Geoinfomatics, University Münster.
Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T. (1988). Numerical Recipes in C - The Art of Scientific Computing. Cambrigde, Cambridge University Press.
Siler, W. and Buckley, J.J. (2005). Fuzzy Expert Systems and Fuzzy Reasoning, Wiley Press.
Viertl, R. (2002). On the Description and Analysis of Measurements of Continuous Quantities. Kybernetika 38(3): 353-362.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Navratil, G., Karimipour, F., Frank, A.U. (2008). Lifting Imprecise Values. In: Bernard, L., Friis-Christensen, A., Pundt, H. (eds) The European Information Society. Lecture Notes in Geoinformation and Cartography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78946-8_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-78946-8_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78945-1
Online ISBN: 978-3-540-78946-8
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)