Zhuravel S. Methods and algorithms for solving continuous problems of optimal partitioning of sets with fuzzy parameters

Thesis submitted for a candidate’s degree in physical-mathematical sciences by specialty 01.05.01 – theoretical bases of information and cybernetics. – Oles Honchar Dnipro National University, Ministry of Education and Science of Ukraine. – Dnipro, 2019. The dissertation is devoted to the development and substantiation of methods and algorithms to solve continuous linear problems of optimal partitioning of sets from n-dimensional Euclidean space into subsets with fuzzy parameters in the target functionals. Based on the improved method of constructing a generalized mathematical model of neuro-linguistic identification of non-linear objects and modifications of N. Z. Shor's -algorithm, there has been defined: – the method of solving a continuous linear one-product problem of optimal partitioning of sets from -dimensional Euclidean space into subsets is devel-oped and theoretically grounded, with the allocation of these subsets’ centers coor-dinates by the presence of constraints in the form of equalities and inequalities, where the target functional has fuzzy parameters; – the method of solving a continuous linear one-product problem of optimal partitioning of sets into subsets is developed and theoretically grounded, with the allocation of these subsets’ centers coordinates with the neuro-linguistic identifica-tion of the functions included in the target functional, where explicit analytical form of these functions is unknown. The Neuro Fuzzy Identification software has been created in object-oriented programming languages C # and Python in the Microsoft Visual Studio 2013 Py-Charm Community Edition development environments, where all developed in the dissertation algorithms are implemented. The methods and algorithms developed in the dissertation have been ap-pliedto solve some practical problems with fuzzy parameters. Keywords: optimal partitioning of sets, neuro-fuzzy technologies, modified N. Z. Shor's -algorithm.