The theoretical framework of nonlinear metrology is he developed in the article. The problem of definition of Shannon entropy and entropic uncertainty interval for measurement results of dynamic variables of nonlinear dynamic systems. It is shown that the correctness of this problem solution depends on the correct determination of the density distribution of the measured values. It is proposed to use interval methods of mathematical analysis, in particular, the histogram distribution for determination of probability density. The principles and formulas of determination the probability density, entropy and entropic uncertainty interval are described.
measurement uncertainty, Shannon entropy, nonlinear dynamical systems, interval analysis