DOI
10.34229/KCA2522-9664.26.5.7
UDC 519.8
E. Kiseleva
Oles Honchar Dnipro National University, Dnipro, Ukraine,
kiseleva47@ukr.net
O. Prytomanova
Kyiv National Economic University named after Vadym Hetman, Kyiv,
Ukraine, prytomanova.olga@kneu.edu.ua
D. Lebediev
Oles Honchar Dnipro National University, Dnipro, Ukraine,
mstr.danila@gmail.com
FUZZY TWO-STAGE CONTINUOUS-DISCRETE PROBLEM OF OPTIMAL SET PARTITION.
II. SOLUTION ALGORITHM AND ITS SOFTWARE IMPLEMENTATION
Abstract. An algorithm for solving a fuzzy two-stage continuous-discrete optimal set partitioning problem has been developed,
which is based on the synthesis of the theory of optimal set partitioning and the theory of fuzzy sets.
The fuzzy optimal set partitioning problem is understood in the sense of finding such a set of fuzzy subsets
of the initial set that in a certain sense minimizes some objective functional.
The fuzzy problem is reduced to finding the degrees of membership of the elements of the initial set to the desired fuzzy subsets,
which together determine the fuzzy partitioning. The components of the developed algorithm are Shor’s r-algorithm for non-differentiable optimization (at the first stage of the problem) and the potential method (at the second stage). The features of the software implementation of the developed algorithm in C++ using the OpenCL parallel computing platform, the OpenGL graphics platform, and the Boost. Multiprecision library are highlighted.
Test examples are provided to confirm the correct operation of the developed algorithm.
Keywords: infinite-dimensional transportation problem, two-stage, continuous problems of optimal partitioning
of set from En, uncertainty, membership function, fuzziness coefficient, degree of distrust, Shor’s r-algorithm, potential method.
full text
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