APPLICATION OF THE THEORY OF OPTIMAL SET PARTITIONING BEFORE BUILDING MULTIPLICATIVELY WEIGHTED VORONOI DIAGRAM WITH FUZZY PARAMETERS (30-35)

DOI: 10.31618/ESU.2413-9335.2020.6.71.615

Дата публикации статьи в журнале: 2020/03/16

Название журнала: Евразийский Союз Ученых — публикация научных статей в ежемесячном научном журнале, Выпуск: 71, Том: 6, Страницы в выпуске: 30-35

Автор: Kiseleva E.M.
, Oles Honchar Dnipro National University ,

Автор: Prytomanova O.M.
, Oles Honchar Dnipro National University ,

Автор: Padalko V.H.
, Oles Honchar Dnipro National University ,

Анотация: An algorithm for constructing a multiplicatively weighted Voronoi diagram involving fuzzy parameters with the optimal location of a finite number of generator points in a limited set of n-dimensional Euclidean space ?? has been suggested in the paper. The algorithm has been developed based on the synthesis of methods of solving the problems of optimal set partitioning theory involving neurofuzzy technologies modifications of N.Z. Shor ? -algorithm for solving nonsmooth optimization problems.

Ключевые слова: multiplicatively weighted Voronoi diagram, optimal set partitioning problem,optimal location of generator points,neurofuzzy technologies,N.Z. Shor r-algorithm,nonsmooth optimization problems,

Данные для цитирования: Kiseleva E.M. Prytomanova O.M. Padalko V.H. . APPLICATION OF THE THEORY OF OPTIMAL SET PARTITIONING BEFORE BUILDING MULTIPLICATIVELY WEIGHTED VORONOI DIAGRAM WITH FUZZY PARAMETERS (30-35) // Евразийский Союз Ученых — публикация научных статей в ежемесячном научном журнале. Физико-математические науки. 2020/03/16; 71(6):30-35. 10.31618/ESU.2413-9335.2020.6.71.615

Скачать в формате PDF

Список литературы: 1.Preparata F., Sheimos M. Computational geometry: an introduction. Springer. First Edition edition, 1993. 390 p. 2.Kiseleva Е.М., Koriashkina L.S. Theory of continuous optimal set partitioning problems as a universal mathematical formalism for constructing Voronoi diagrams and their generalizations I. Theoretical foundations // Cybernetics and Systems Analysis, vol. 51, № 3, pp. 325-335 (2015). DOI 10.1007/s10559-015-9725-x. 3.Kiseleva Е.М., Koriashkina L.S. Theory of continuous optimal set partitioning problems as a universal mathematical formalism for constructing voronoi diagrams and their generalizations. II. Algorithms for constructing Voronoi diagrams based on the theory of optimal set partitioning // Cybernetics and Systems Analysis, vol. 51, № 4, pp. 489-499 (2015). DOI: 10.1007/s10559-015-9740-y. 4. Aurenhammer F., Klein R., Lee D.-T. Voronoi Diagrams and Delaunay Triangulations. World Scientific Pub Co Inc, 2013. 337 p. 5.Okabe A., Boots B, Sugihara K., Chiu S.N. Spatial Tessellations: Concepts and Applications of Voronoi Diagrams // West Sussex, England: John Wiley and Sons Ltd, second ed., 2000. 696 p. 6.Trubin Stanislav I. Information Space Mapping with Adaptive Multiplicatively Weighted Voronoi Diagrams // Thesis (M.S.) – Origon State University. – 2007. 7.Kiseleva E.M., Shor N.Z. Сontinuous problems of optimal set partitioning: theory, algorithms, applications. Kyiv: Naukova Dumka, 564 p. (2005) [in Russian]. 8.Kiseleva E.M., Pritomanova O.M., Zhuravel S.V. Algorithm for Solving a Continuous Problem of Optimal Partitioning with Neurolinguistic Identification of Functions in Target Functional // Journal of Automation and Information Science, vol. 50, № 3, pp. 1-20 (2018). DOI: 10.1615/JAutomatInfScien.v50.i3.10. 9.Shor, N.Z. Nondifferentiable optimization and polynomial problems. Boston; Dordrecht; London: Kluwer Acad. Publ., 412 p. (1998) 10. Stetsyuk P.I. Shor’s r-Algorithms: Theory and Practice. In: Optimization Methods and Applications: In Honor of the 80th Birthday of Ivan V. Sergienko. Ed. by Butenko S., Pardalos P.M, Shylo V. Springer. 2017. P. 495–520. 11. Kiseleva E., Hart L., Prytomanova O., Kuzenkov О. An Algorithm to Construct Generalized Voronoi Diagrams with Fuzzy Parameters Based on the Theory of Optimal Partitioning and Neuro-Fuzzy Technologies. URL: http://ceur-ws.org/Vol- 2386/paper12.pdf.