Prytomanova O. Fuzzy problems of optimal set partitioning: theoretical bases, methods and algorithms for solving

The dissertation is devoted to the further development of the theory of optimal programming with Boolean variables, for fuzzy optimal partition problems, in which computational intelligence methods are used in purpose to reveal uncertainty: fuzzy set theory and fuzzy neural networks. Developed and theoretically substantiated methods and algorithms for solving problems of optimal partitioning of sets (both in terms of certainty and uncertainty) in complex formulations, namely: with additional restrictions on the subsets centers location, two-stage continuous-discrete placement-partition problem. Algorithms for constructing generalized, additively and multiplicatively weighted Voronoi diagrams with optimal placement of generator points in a limited set of -dimensional Euclidean space both under conditions of certainty and with fuzzy initial data is developed. Methods and algorithms for solving problems of optimal division of a clear set into fuzzy subsets are developed and theoretically substantiated. The proposed algorithms are based on the synthesis of methods for the theory of optimal partitioning of sets with neurofuzzy technologies and Shor’s r-algorithm modifications in order to solve non-differential optimization problems. Complexes of computer programs for realization of the proposed decision of optimum partitioning problems are developed.