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Standard Interval Computation Algorithm Is Not Inclusion-Monotonic: Examples

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Uncertainty, Constraints, and Decision Making

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 484))

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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 come 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.

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Acknowledgements

This work was supported in part by the National Science Foundation grants 1623190 (A Model of Change for Preparing a New Generation for Professional Practice in Computer Science), and HRD-1834620 and HRD-2034030 (CAHSI Includes), and by the AT&T Fellowship in Information Technology.

It was also supported by the program of the development of the Scientific-Educational Mathematical Center of Volga Federal District No. 075-02-2020-1478, and by a grant from the Hungarian National Research, Development and Innovation Office (NRDI).

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Correspondence to Vladik Kreinovich .

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Mizukoshi, M.T., Lodwick, W., Ceberio, M., Kreinovich, V. (2023). Standard Interval Computation Algorithm Is Not Inclusion-Monotonic: Examples. In: Ceberio, M., Kreinovich, V. (eds) Uncertainty, Constraints, and Decision Making. Studies in Systems, Decision and Control, vol 484. Springer, Cham. https://doi.org/10.1007/978-3-031-36394-8_63

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