Abstract
This paper considers a model of a multidimensional space, in which variables are ordered and contain a finite number of values. Such a space may be analyzed with the n-tuple algebra developed by the authors as a natural combination of methods for the analysis of n-ary relations and logical structures. Some approaches enabling the application of some cluster analysis methods are proposed for this model.
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Funding
The work was supported in part by the Russian Foundation for Basic Research (project nos. 18-07-00132, 18-01-00076, 18-29-03022, and 19-08-00079).
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Boris Aleksandrovich Kulik was born in 1941 and graduated from the Leningrad Mining Institute in speciality “Technique for the Exploration of Mineral Deposits” in 1963. He received a candidate’s degree in engineering in 1996 and a doctoral degree in physics and mathematics in 2008. He has worked in the Institute of Problems of Mechanical Engineering of the Russian Academy of Sciences (St. Petersburg) since 1997, currently as a leading researcher. He is a member of the Russian Association of Artificial Intelligence. He has acknowledgments and awards, is the author of more than 150 papers, among which 4 inventions, 5 monographies (3 of them with coauthors), and 4 chapters in monographies. His scientific interests include: logic, artificial intelligence, and logical-probabilistic analysis.
Aleksandr Yakovlevich Fridman was born in 1952, and graduated from the Leningrad Electrotechnical Institute in speciality “Gyroscopic Instruments and Devices” in 1975. He received a candidate’s degree in engineering in 1986, and a doctoral degree in engineering in 2002. He became a professor of the Department of Applied Mathematics in 2008. His primary employment is at the Institute for Informatics and Mathematical Modeling of the Kola Scientific Center of the Russian Academy of Sciences as a leading researcher. His scientific interests include: modeling of complex technologies and their environmental effect and applied intellectualized systems. He is the author of more than 320 papers, among which 16 inventions, 5 monographies, 4 chapters in monographies, and 24 educational and 29 scientific works used in pedagogical practice. He is a member of Academic Senates at the Institute of Informatics of Mathematical Modeling of Engineering Processes and the Center for the Physical and Technical Problems of Power Engineering in the North of the Kola Scientific Center of the Russian Academy of Sciences. Member of the Russian Association of Artificial Intelligence, expert of the Ministry of Industry and Energy of the Russian Federation in the basic industry branches for the region, and expert of the Russian Foundation for Basic Research. He was awarded with Honorary Certificates from the Ministry of Education and Science of the Russian Federation and the Murmansk Region Duma to the 75th Anniversary of the Kola Scientific Center of the Russian Academy of Sciences, the Governor of the Murmansk region, the Petrozavodsk State University. He has acknowledgments and awards.
Translated by E. Glushachenkova
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Kulik, B.A., Fridman, A.Y. Methods of Clustering on Logical Models. Pattern Recognit. Image Anal. 30, 203–210 (2020). https://doi.org/10.1134/S1054661820020091
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DOI: https://doi.org/10.1134/S1054661820020091