Empirical reconstruction of a fuzzy model and the reduction of measurements in Euclidean metric

In the framework of a fuzzy model being refined by test measurements, experimental data are reduced to a form characteristic for measurements made by an ideal measuring device. A model of a measurement error is formulated in terms of fuzzy constraints imposed on its Euclidean norm. The solution of the reduction problem is illustrated by the example of a photosynthetic system when the measured parameters are the amount of the synthesized adenosine triphosphate and the mean concentration of protons and the parameter under estimation is the time period during which the reduced measurements are obtained. The work was supported by the Russian Foundation for Basic Research (projects 11-07-00338, 09-01-96508, and 09-07-00505).