Application of optimal set partitioning theory to solving problems of artificial intelligence and pattern recognition

Authors

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2021.4.07

Keywords:

pattern recognition, artificial intelligence, fuzzy Voronoi diagram, point generators, optimal set partitioning, infinite-dimensional mathematical programming

Abstract

The paper substantiates the possibility of applying the mathematical theory of continuous problems of optimal partitioning of sets of n-dimensional Euclidean space, which belong to the non-classical problems of infinite-dimensional mathematical programming, to the solution of problems of artificial intelligence and pattern recognition. The problems of pattern recognition both in conditions of certainty and in conditions of uncertainty are formulated. A particular attention is paid to the application of methods of the theory of optimal partitioning for the construction of fuzzy Voronoi diagrams. Examples of constructing fuzzy Voronoi diagrams with the optimal placement of generating points are given.

Author Biographies

Elena Kiseleva, Oles Honchar Dnipro National University, Dnipro

Elena M. Kiseleva,

Corresponding Member of the National Academy of Sciences of Ukraine, Professor, Doctor of Physical and Mathematical Sciences, the Dean of the Faculty of Applied Mathematics of Oles Honchar Dnipro National University, Dnipro, Ukraine.

Olga Prytomanova, Oles Honchar Dnipro National University, Dnipro

Olga M. Prytomanova,

associate professor, Doctor of Physical and Mathematical Sciences, a professor at the Department of Computational Mathematics and Mathematical Cybernetics of Oles Honchar Dnipro National University, Dnipro, Ukraine.

Liudmyla Hart, Oles Honchar Dnipro National University, Dnipro

Liudmyla L. Hart,

Doctor of Physical and Mathematical Sciences, a professor at the Department of Computational Mathematics and Mathematical Cybernetics of Oles Honchar Dnipro National University, Dnipro, Ukraine.

References

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Published

2021-12-22

Issue

Section

Methods of optimization, optimum control and theory of games