Abstract
For a numerical physical quantity v, because of the measurement imprecision, the measurement result \(\widetilde v\) is, in general, different from the actual value v of this quantity. Depending on what we know about the measurement uncertainty \(\Delta v\stackrel{\rm def}{=}\widetilde v-v\), we can use different techniques for dealing with this imprecision: probabilistic, interval, etc.
When we measure the values v(x) of physical fields at different locations x (and/or different moments of time), then, in addition to the same measurement uncertainty, we also encounter another type of localization uncertainty: that the measured value may come not only from the desired location x, but also from the nearby locations.
In this paper, we discuss how to handle this additional uncertainty.
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References
Anderson, E.J., Nash, P.: Linear Programming in Infinite-Dimensional Spaces. Wiley, New York (1987)
Anguelov, R., Markov, S., Sendov, B.: The set of Hausdorff continuous functions – the largest linear space of interval functions. Reliable Computing 12, 337–363 (2006)
Averill, M.G.: A Lithospheric Investigation of the Southern Rio Grande Rift, PhD Dissertation, University of Texas at El Paso, Department of Geological Sciences (2007)
Jaulin, L., et al.: Applied Interval Analysis. Springer, London (2001)
Kuznetsov, V.: Interval Statistical Methods. Radio i Svyaz Publ., Moscow (1991) (in Russian)
Perfilieva, I.: Fuzzy transforms: theory and applications. Fuzzy Sets and Systems 157, 993–1023 (2006)
Perfilieva, I., Novák, V., Dvorák, A.: Fuzzy transform in the analysis of data. International Journal of Approximate Reasoning 48(1), 36–46 (2008)
Pinheiro da Silva, P., et al.: Propagation and Provenance of Probabilistic and Interval Uncertainty in Cyberinfrastructure-Related Data Processing and Data Fusion. In: Muhanna, R.L., Mullen, R.L. (eds.) Proceedings of the International Workshop on Reliable Engineering Computing REC 2008, Savannah, Georgia, February 20-22, pp. 199–234 (2008)
Walley, P.: Statistical Reasoning with Imprecise Probabilities. Wiley, Chichester (1991)
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Kreinovich, V., Perfilieva, I. (2010). From Gauging Accuracy of Quantity Estimates to Gauging Accuracy and Resolution of Measuring Physical Fields. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2009. Lecture Notes in Computer Science, vol 6068. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14403-5_48
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DOI: https://doi.org/10.1007/978-3-642-14403-5_48
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14402-8
Online ISBN: 978-3-642-14403-5
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