<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The paper presents a method of determining the robustness of solutions of systems of interval linear equations (ILEs). The method can be applied also for the ILE systems for which it has been impossible to find solutions so far or for which solutions in the form of improper intervals have been obtained (which cannot be implemented in practice). The research conducted by the authors has shown that for many problems it is impossible to arrive at ideal solutions that would be fully robust to data uncertainty. However, partially robust solutions can be obtained, and those with the highest robustness can be selected and put into practice. The paper shows that the degree of robustness to the uncertainty of the entire system can be calculated on the basis of the degrees of robustness of individual equations, which greatly simplifies calculations. The presented method is illustrated with a series of examples (also benchmark ones) that facilitate its understanding. It is an extension of the authors’ previously published method for first-order ILEs.</p>
</abstract>

The paper presents a method of determining the robustness of solutions of systems of interval linear equations (ILEs). The method can be applied also for the ILE systems for which it has been impossible to find solutions so far or for which solutions in the form of improper intervals have been obtained (which cannot be implemented in practice). The research conducted by the authors has shown that for many problems it is impossible to arrive at ideal solutions that would be fully robust to data uncertainty. However, partially robust solutions can be obtained, and those with the highest robustness can be selected and put into practice. The paper shows that the degree of robustness to the uncertainty of the entire system can be calculated on the basis of the degrees of robustness of individual equations, which greatly simplifies calculations. The presented method is illustrated with a series of examples (also benchmark ones) that facilitate its understanding. It is an extension of the authors’ previously published method for first-order ILEs.

A Realistic Tolerant Solution of a System of Interval Linear Equations with the Use of Multidimensional Interval Arithmetic

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The paper presents a method of determining the robustness of solutions of systems of interval linear equations (ILEs). The method can be applied also for the...

A Realistic Tolerant Solution of a System of Interval Linear Equations with the Use of Multidimensional Interval Arithmetic

Published Online: Jun 23, 2023

Page range: 229 - 247

Received: Jul 26, 2022

Accepted: Feb 02, 2023

DOI: https://doi.org/10.34768/amcs-2023-0018

Keywords
interval arithmetic, interval linear equation system, tolerable solution, multidimensional interval arithmetic

© 2023 Andrzej Piegat et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A Realistic Tolerant Solution of a System of Interval Linear Equations with the Use of Multidimensional Interval Arithmetic

Published Online: Jun 23, 2023

Page range: 229 - 247

Received: Jul 26, 2022

Accepted: Feb 02, 2023

DOI: https://doi.org/10.34768/amcs-2023-0018

Keywordsinterval arithmetic, interval linear equation system, tolerable solution, multidimensional interval arithmetic

© 2023 Andrzej Piegat et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
interval arithmetic, interval linear equation system, tolerable solution, multidimensional interval arithmetic