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Registration Number

0220U101872, 0119U100600 , R & D reports

Title

Development of mathematical models and algorithms for the solution of classification, clustering applied problems based on the theory of optimal partitioning of sets

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Head

Kiseleva Elena M., Доктор фізико-математичних наук

Registration Date

27-02-2020

Organization

Oles Honchar Dnipro National University

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 Object of the study is the processes of creating new mathematical models of complex phenomena and systems that lead to problems of classification, clustering, partitioning. The purpose of the study is to obtain new mathematical models of fuzzy continuous optimal set partitioning (OSP) problems adapted to the problems of predictive estimation in geodynamics and thin-walled structures; to study the properties of constructed mathematical models. Methods of mathematical modeling, of infinite-dimensional mathematical programming, of non-differentiable optimization were used as the research methods during the execution of the stage. Theoretical results of the study are new mathematical formulations of both clear and fuzzy continuous OSP problems (single-product and multi-product ones, with the given location of the centers of subsets and with their search, without constraints and with imposed constraints) adapted to the problems of predictive estimation in the geodynamics and mechanics of thin-walled systems; properties of the obtained mathematical models of classification and partitioning problems; All stage studies are conducted for the first time and have no analogues and prototypes for meaningful comparison. The obtained scientific results are new, they satisfy the requirements related to the development of such a plan in the world science and they are accompanied with detailed techniques. The obtained results were used in the educational process of the Oles Honchar Dnipro National University during the development and implementation of new cycles of laboratory work and lecture courses of four normative and selective subjects in the training of specialists in 124 System analysis and 113 Applied mathematics. Application area – research and experimental development on other natural sciences and engineering.

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Baleyko Natalia V.
Hart Liudmyla L
Zhuravel Serhiy V.
Kolodyazhniy Anatoliy P.
Kuzenkov Olexandr O.
Prytomanova Olga M.
Yatsechko Natalia Ye

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2020-04-02