Програмна реалізація алгоритму розв’язання динамічної задачі оптимального розбиття множин в умовах невизначеності

Purpose. Among various formulations of the optimal set partitioning (OSP) problem, dynamic variants—where optimization conditions change over time—are of particular interest due to their relevance for real-world applications. Such systems often operate under uncertainty, which may arise from imprecise or incomplete input data, vague parameters, or unreliable mathematical representations of system behavior. This study develops a comprehensive mathematical and computational framework for solving dynamic OSP problems under uncertainty. The aim of the study is to develop software for solving a novel dynamic optimal set partitioning problem under uncertainty, specifically including the formulation of a numerical experiment, the applied interpretation of the obtained results, and a comparative analysis of the numerical experiment outcomes with the analytical results of the model investigation. Methodology. The methodological basis of the study consists of the principles of optimal set partitioning theory and fuzzy set theory. Modern numerical methods were used to solve systems of ordinary differential equations necessary for determining the parameters of the dynamic model. Findings. The formulation of dynamic optimal set partitioning problems under uncertainty allows including fuzzy model parameters and obtaining results even with incomplete information about the system. The work presents a clearly defined algorithm for solving the problem, determined by its mathematical formulation. Originality. The proposed models represent a significant contribution to the development of mathematical modeling, particularly in dynamic and fuzzy problem formulations. Methods and algorithms for solving the formalized problems are presented, and the results of comparative analysis allow assessing the analytical and numerical advantages of both models and the dynamic approach to solving such problems. Practical value. The practical value of the results obtained in this study lies in the formulation of a novel dynamic optimal set partitioning problem under uncertainty, the development of software for the numerical implementation of the experiment, and the visualization of the obtained results. The formalized mathematical model and the developed software can be applied to a wide range of practical problems, such as logistics, facility location, partitioning of communities into administrative service centers, and others.