"Empirical reconstruction of a fuzzy model and the reduction of measurements in uniform metric"
Kopit T.A., Chulichkov A.I., Ustinin D.M.

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-a).

Keywords: mathematical modeling, decision making, analysis and interpretation of data, measurement and computing systems, theory of possibilities, fuzzy element

Kopit T.A.   e-mail: kopit_tanya@mail.ru;   Chulichkov A.I.   e-mail: achulichkov@gmail.com
Ustinin D.M.   e-mail: ustinin@mail.ru