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01.10.2019 | MATHEMATICAL THEORY OF PATTERN RECOGNITION | Ausgabe 4/2019

Pattern Recognition and Image Analysis 4/2019

Subjective Restoration of Mathematical Models for a Research Object, Its Measurements, and Measurement-Data Interpretation

Zeitschrift:
Pattern Recognition and Image Analysis > Ausgabe 4/2019
Autoren:
Yu. P. Pyt’ev, O. V. Falomkina, S. A. Shishkin
Wichtige Hinweise
https://static-content.springer.com/image/art%3A10.1134%2FS1054661819040138/MediaObjects/11493_2019_6025_Fig8_HTML.gif
Yuri Petrovich Pyt’ev. Born in 1935. Graduated from the Faculty of Physics at Lomonosov Moscow State University in 1959. Received Ph.D. in theoretical and mathematical physics from Lomonosov Moscow State University in 1963 and Doctor of Sciences degree in 1976. Head of the Mathematical Modeling and Informatics Department (earlier, Computer Methods in Physics) at the Faculty of Physics of MSU from 1995 to 2018. Professor of the Mathematical Modeling and Informatics Department since 2018. Scientific interests: fuzzy and uncertain fuzzy mathematics, theory of possibilities, subjective modeling, mathematical modeling, image processing, pattern recognition and image analysis. Author of more than 400 papers and 30 books.
https://static-content.springer.com/image/art%3A10.1134%2FS1054661819040138/MediaObjects/11493_2019_6025_Fig9_HTML.gif
Olesya Vladimirovna Falomkina. Born in 1979. Graduated from the Faculty of Physics at Lomonosov Moscow State University in 2002. Received Ph.D. in mathematical modeling, numerical methods, and software development from Lomonosov Moscow State University in 2006. Senior Researcher of the Mathematical Modeling and Informatics Department (earlier, Computer Methods in Physics) at the Faculty of Physics of MSU since 2005. Scientific interests: fuzzy and uncertain fuzzy mathematics, theory of possibilities, mathematical modeling, image processing, pattern recognition and image analysis. Author of more than 20 papers.
https://static-content.springer.com/image/art%3A10.1134%2FS1054661819040138/MediaObjects/11493_2019_6025_Fig10_HTML.gif
Semen Aleksandrovich Shishkin. Born in 1993. Graduated from the Faculty of Physics at Lomonosov Moscow State University in 2018. Engineer of the Mathematical Modeling and Informatics Department (earlier, Computer Methods in Physics) at the Faculty of Physics of MSU since 2019. Scientific interests: pattern recognition and image analysis, mathematical modeling, fuzzy and uncertain fuzzy mathematics, theory of possibilities, and image processing. Author of 5 papers.
Translated by I. Tselishcheva

Abstract

The problems of empirical reconstruction of the subjective model of a research object (RO), the subjective model of its measurements, their subjective analysis, and subjective interpretation of the measurement data are considered. To solve these problems, we use the mathematical formalism for subjective modeling (MFSM), subjective judgments made by the researcher–modeler (r.–m.) concerning the mathematical model of the RO and its measurements and based on his scientific experience and intuition. The subjective models of measurements of the RO and measurement-data interpretation are defined by the r.–m. as elements of a parametric family of smoothing splines. It is shown that the maximum posterior accuracy of the subjective interpretation of the measurement-experiment data, which is “observed” in the solution process for the problems of restoring the subjective models of the RO and its measurements, analysis, and measurement-data interpretation, can serve as a criterion for the truth of the subjective models of the measurement experiment and interpretation of the obtained measurement data, since the criterion for the accuracy of measurement-data interpretation is not used in the reconstruction of the above models. The paper suggests the principle of the maximum posterior accuracy of the subjective interpretation of measurement-experiment data as a criterion for the adequacy of subjectively reconstructed models of measurement experiments and interpretation of measurement data.

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