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Numerical methods and programming, 2011, Volume 12, Issue 1, Pages 90–96
(Mi vmp172)
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Вычислительные методы и приложения
Empirical reconstruction of a fuzzy model and the reduction of
measurements in uniform metric
T. A. Kopita, A. I. Chulichkova, D. M. Ustininb a M. V. Lomonosov Moscow State University, Faculty of Physics
b Department of Biology, M.V. Lomonosov Moscow State University
Abstract:
A linear scheme of a measuring experiment is considered. A measurement result is
interpreted as the output signal of the measuring device distorted by an additive
error. A new method is proposed for reducing a measurement to the form peculiar
to measurements
made by an ideal measuring device. A mathematical model of the measuring device that
associates the measurement result with its input signal is unknown; the information
on the model is extracted from the results of test experiments. A measurement error
is described in terms of the theory of possibilities. The reduction problem is
formulated as a problem of finding the maximum of a posteriori possibility. A
computational algorithm is proposed. The algorithm operation is illustrated by an
example of data analysis for a biophysical computer experiment intended to simulate
a photosynthetic system and to estimate the time of synthesis on the basis of the
amount of the synthesized adenosine triphosphate. The work was supported by the
Russian Foundation for Basic Research (projects 11-07-00338 and 09-07-00505.
Keywords:
mathematical modeling; decision making; analysis and interpretation of data; measurement and computing systems; theory of possibilities; fuzzy element.
Citation:
T. A. Kopit, A. I. Chulichkov, D. M. Ustinin, “Empirical reconstruction of a fuzzy model and the reduction of
measurements in uniform metric”, Num. Meth. Prog., 12:1 (2011), 90–96
Linking options:
https://www.mathnet.ru/eng/vmp172 https://www.mathnet.ru/eng/vmp/v12/i1/p90
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