This article discusses the application of an interval approach in solving problems in the field of physics, particularly spectral analysis. To process data with interval uncertainty, a linear interval tolerance problem is modeled, and the inconsistency (unsolvability) of an interval system of linear algebraic equations (ISLAE) with the use of a recognizing functional is presented. The actual regularization problem of the inconsistent interval systems of linear equations is solved. The idea of a combined method for correcting a linear interval tolerance problem, formulated by S. Shary, is implemented. A new method for controlling the solution of an ISLAE was developed by changing the radii of the matrix elements of the system. The research results can be used, for example, to calculate the concentrations of substances through the measurement of characteristic x-ray radiation.