Data analysis with interval uncertainty: application of a combined sampling measure

One of the main tasks of data analysis is to estimate the parameters of a data sample of the constant physical value. Data analysis is required in all areas of experimental physics to obtain reliable measurement results. To describe sample elements with interval uncertainty, the technique of interval analysis and interval statistics is used. In particular, the homogeneity of data in a sample is described using various measures of similarity. A set of three coherence measures is presented that describe different relationships of sample elements. Based on the considered set, a combined measure of sample similarity is proposed, which allows one to simultaneously find external and internal estimates of the value under study. These estimates are important for solving a massive data processing problem, when the sets of samples are obtained under different measurement conditions. The necessary information about interval analysis and various interval arithmetic is provided. The relations between the proposed combined measure and the results of calculations with interval twins and fuzzy sets are considered. This combined measure can be used when solving a massive data processing problem typical for practical and scientific areas of semiconductor physics. A practical example of the use of a combined sample consistency measure when testing solar radiation converters against a reference converter is given as part of the study of their spectral properties and quantum yield.

1. Bazhenov A. N., Telnova A. Yu., Measurement Techniques, 2023, vol. 65, no. 12, pp. 882–890. https://doi.org/10.1007/s11018-023-02180-2

2. Bazhenov A. N., Zhilin S. I., Kumkov S. I., Shary S. P., Obrabotka i analiz interval’nich dannyсh, Моscow, Izhevsk, NIC Regulyarnaya i haoticheskaya dinamika Publ., 2023, 374 p.

3. Shary S. P., Data fi tting problem under interval uncertainty in data, Industrial laboratory. Diagnostics of materials, 2020, vol. 86(1), pp. 62–74. (In Russ.)

4. Shary S. P., Konechnomernyj interval’nyj analiz, Novosibirsk, XYZ Publ., 2022, 622 p. (In Russ.)

5. Kearfott R. B., Nakao M. T., Neumaier A., Rump S. M., Shary S. P., van Hentenryck P., Standardized notation in interval analysis, Journal of Computational Technologies, 2010, vol. 15, no 1, pp. 7–13.

6. Shary S., Numerical computation of formal solutions to interval linear systems of equations, arXiv:1903.10272v1 [math.NA] 15 Mar 2019, https://doi.org/10.48550/arXiv.1903.10272

7. Nesterov V. M. Doctoral dissertation Mathematics and Physics Sciences ( St. Petersburg Institute of Informatics and Automation of the Russian Academy of Sciences, St. Peters-burg, 1999).

8. Oskorbin N. M., Maksimov A. V., Zhilin S. I., Construction and analysis of empirical dependencies by the method of the center of uncertainty, Izvestiya of Altai State University, 1998, no. 1, pp. 35–38. (In Russ.)

9. Ibragimov V. A., Elements of fuzzy mathematics. Monograph. Baku, AGNA, 2010, 394 p.

10. Zhilin S. I. Candidate’s dissertation Mathematics and Physics Sciences (Altai State University, Barnaul, 2004).

11. Iavoruk T., Bazhenov A., The use of twins in isotopic analysis, Proceedings of 12th International Conference on Mathematical Modelling in Physical Sciences, August 28–31, 2023, Belgrade, Serbia Springer Proceedings in Mathematics and Statistics, 2024 (accepted, in publications), available at: https://www.icmsquare.net/index.php/program/submissions (accessed: 01.11.2023).

12. Luciano da F. Costa. Mulsetions and Intervalions: Multiset Generalizations of Functions. September, 2023, Preprint, available at: https://www.researchgate.net/publication/373772964_Mulsetions_and_Intervalions_Multiset_Generalizations_of_Functions (accessed: 31.10.2023).