In this paper we introduce a method for the empirical reconstruction of a fuzzy model of measurements on the basis of testing measurements using a possibility-theoretical approach. The method of measurement reduction is developed for solving a problem of an estimation of parameters of a fuzzy system. It is shown that such problems are reduced to minimax problems. If the model is unknown it can be restored from testing experiments and can be applied for handling the problems of the type of forecasting the behavior of a system.

In this paper we introduce a method for the fuzzy model reconstruction and a method for measurements reduction on the basis of test signals by maximization a posteriori possibility. It ensures the maximum accuracy of the measurements reduction. It is used the model of measurement errors with fuzzy constraints on its Euclidean norms.

Methods for estimating the input signal of a measuring device are considered. Information about the device is contained in the measurement results of a set of known test signals and the measurements were obtained in natural or in computational experiments. A method is proposed for the approximation of the measurement model by means of a piecewise linear model that is consistent with the results of measurements and the method of evaluation of the input signal and its accuracy. An example is given of the solution of a problem of the interpretation of measurements based on the approximation of a model of the photosynthetic system, in which the measured parameters are the values of saturation ΔpH and the rate of ATP synthesis and the estimated parameters are the concentration of photosystem-2 and light intensity.