How Interval Measurement Uncertainty Affects the Results of Data Processing: A Calculus-Based Approach to Computing the Range of a Box
Andrzej Pownuk, V. Kreinovich · Matematičeskie struktury i modelirovanie · 2018
In many practical applications, we are interested in the values of the quantities y1,...,ymwhich are difficult (or even impossible) to measure directly. A natural idea to estimate these values is to find easier-to-measure related quantities x1,...,xn and to use the known relation to estimate the desired values yj. Measurements come with uncertainty, and often, the only thing we know about the actual value of each auxiliary quantity xiis that it belongs to the interval [xi,xi] = [̃︀ xi-Δi, ̃︀ xi+Δi], where ̃︀ xiis the measurement result, and Δiis the upper bound on the absolute value of the measurement error ̃︀ xi- xi. In such situations, instead of a single value of a tuple y = (y1,...,ym), we have a range of possible values. In this paper, we provide calculus-based algorithms for computing this range.