How Interval Measurement Uncertainty Affects the Results of Data Processing: A Calculus-Based Approach to Computing the Range of a Box

Authors

Andrew Pownuk, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

4-2018

Comments

Technical Report: UTEP-CS-18-39

Published in Mathematical Structures and Modeling, 2018, Vol. 46, pp. 118-124.

Abstract

In many practical applications, we are interested in the values of the quantities y₁, ..., y_m which are difficult (or even impossible) to measure directly. A natural idea to estimate these values is to find easier-to-measure related quantities x₁, ..., x_n and to use the known relation to estimate the desired values y_i. Measurements come with uncertainty, and often, the only thing we know about the actual value of each auxiliary quantity x_i is that it belongs to the interval [X_i − Δ_i, X_i + Δ_i], where X_i is the measurement result, and Δ_i is the upper bound on the absolute value of the measurement error Δ x_i = X_i − x_i. In such situations, instead of a single value of a tuple y = (y₁, ..., y_m), we have a range of possible values. In this paper, we provide calculus-based algorithms for computing this range.