A method for reconstructing linearly parameterized (in particular, polynomial) functional dependencies from data with interval uncertainty is developed. In many situations, it provides more adequate processing of imprecise measurement and observation results than traditional probability-theoretic approaches. The proposed method uses the mathematical apparatus of interval analysis and is based on the so-called maximum compatibility principle. It allows efficient construction of nonlinear functional dependencies in the form of generalized polynomials from interval data arising in both dependent and independent variables. As a practical example, the processing of real data from an aluminothermic process for industrial waste utilization is considered, where the new method demonstrates significant advantages compared to the traditional least squares method.
S.P. Sharyy (Wed,) studied this question.