Про динамічну задачу оптимального розбиття множин із фіксованими центрами за умов невизначеності

• Дата: 2025
• Автори: Kiseleva, Elena, Prytomanova, Olha, Kuzenkov, Oleksandr
• Формат: Стаття
• Мова: Ukrainian
• Опубліковано: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2025
• Теми: динамічна задача; теорія оптимального розбиття множин; нечіткий параметр; нейронечіткі технології; нескінченновимірне математичне програмування; недиференційовна оптимізація; методи штучного інтелекту
• Онлайн доступ: https://jais.net.ua/index.php/files/article/view/525
• Назва журналу: Problems of Control and Informatics

Among the various formulations of the optimal set partitioning (OSP) problem, dynamic variants — where the optimization conditions evolve over time — are of particular interest due to their relevance to practical applications. Such systems often operate under uncertainty, which may arise from imprecise or incomplete input data, ambiguous parameters, or unreliable mathematical descriptions of system behavior. In this study, we develop a comprehensive mathematical and computational framework for solving dynamic OSP problems under uncertainty. Our approach integrates the theory of optimal set partitioning with modern artificial intelligence techniques, particularly fuzzy logic, fuzzy set theory, and neuro-fuzzy systems. The proposed method consists of two main stages: neuro-fuzzy identification, which transforms vague and uncertain data in the initial conditions of the problem; and dynamic optimization of the set partitioning based on the refined input. This hybrid approach ensures real-time adaptation of partitioning strategies to a changing environment and uncertain conditions. Potential application areas include clustering, resource allocation, adaptive control, network planning, and decision support in complex dynamic systems. The results contribute to the advancement of robust and adaptive models in mathematical statistics and operations research.