Standard Interval Computation Algorithm Is Not Inclusion-Monotonic: Examples

Authors

Marina Tuyako Mizukoshi, Federal University of GoiasFollow
Weldon Lodwick, University of Colorado DenverFollow
Martine Ceberio, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

12-1-2022

Comments

Technical Report: UTEP-CS-22-125

Abstract

When we usually process data, we, in effect, implicitly assume that we know the exact values of all the inputs. In practice, these values comes from measurements, and measurements are never absolutely accurate. In many cases, the only information about the actual (unknown) values of each input is that this value belongs to an appropriate interval. Under this interval uncertainty, we need to compute the range of all possible results of applying the data processing algorithm when the inputs are in these intervals. In general, the problem of exactly computing this range is NP-hard, which means that in feasible time, we can, in general, only compute approximations to these ranges. In this paper, we show that, somewhat surprisingly, the usual standard algorithm for this approximate computation is not inclusion-monotonic, i.e., switching to more accurate measurements and narrower subintervals does not necessarily lead to narrower estimates for the resulting range.