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Registration Number

0221U102211, 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

Head

Kiseleva Elena M., Доктор фізико-математичних наук

Registration Date

29-01-2021

Organization

Oles Honchar Dnipro National University

Description

 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 infinite-dimensional mathematical programming, of non-differentiable optimization, methods for solving operator equations, methods for solving linear and nonlinear problems of OSP, apparatus and methods of functional analysis were used as the research methods during the execution of the stage. Theoretical results of the study are new methods and algorithms for solving the constructed fuzzy models based on the theory of OSP, both with fixed centers of subsets and with the location of centers using neuro-fuzzy technologies. The obtained scientific results are new, they satisfy the requirements related to the development of such a type in the world science and are accompanied with detailed neuro-fuzzy technologies and techniques. The obtained results were used in the educational process of the Oles Honchar Dnipro National University when teaching 4 general disciplines for students of the Faculty of Applied Mathematics, specialties 124 System analysis and 113 Applied mathematics. Application area 72.19 – Research and experimental development on other natural sciences and engineering.

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Baleyko Natalia V.
Нart Liudmyla L
Zhuravel Serhiy V.
Kuzenkov Olexandr O.
Prytomanova Olga M.
Firsova Tetyana O
Yatsechko Natalia Ye