Abstract
Statements that can be recorded by logical multivalued relations are studied. Using model theory, we introduce relations such that various logical values are taken into account most completely in the distances between relations of Lukasevich n-valued logic, introduce an uncertainty measure for statements, and formulate and prove theorems about the properties of these values. Using the introduced distances and uncertainty measures, we adapt known clustering algorithms for the clustering of sets of statements and use examples to examine results for various values of n. We study collective distances, which are the most effective in the sense of clustering indices and can be used to generate new distances for more powerful sets of statements.
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Aleksandr Aleksandrovich Vikent’ev. Born in 1954. Graduated from the Academician Buketov Karaganda State University in 1977. PhD in model theory, 1992. Associate Professor from the Department of Algebra and Mathematical Logic of Novosibirsk State University, 1997. Senior Scientific Researcher at the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. Author of more than 70 scientific and didactic papers (text-books Number-Theory Problems and Manual for the Turing–Post Machine). Scientific interests: artificial intelligence, computability, model theory, knowledge analysis, pattern recognition, and data clustering.
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Vikent’ev, A.A. New model metrics between relations of n-valued logic and uncertainty of automatic clustering of statements. Pattern Recognit. Image Anal. 27, 404–417 (2017). https://doi.org/10.1134/S1054661817030300
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DOI: https://doi.org/10.1134/S1054661817030300