Open AccessApplication of optimal set partitioning theory to solving problems of artificial intelligence and pattern recognition
Author(s) -
Elena M. Kiseleva,
O. M. Prytomanova,
Liudmyla Hart
Publication year - 2021
Publication title -
sistemnì doslìdžennâ ta ìnformacìjnì tehnologìï
Language(s) - English
Resource type - Journals
eISSN - 2308-8893
pISSN - 1681-6048
DOI - 10.20535/srit.2308-8893.2021.4.07
Subject(s) - voronoi diagram , euclidean geometry , mathematics , fuzzy set , set (abstract data type) , mathematical theory , computer science , artificial intelligence , mathematical optimization , fuzzy logic , physics , geometry , quantum mechanics , programming language
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.