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Abstract

An approach is proposed to solve one continuous linear single-product problem of optimal partitioning of set Ω from n-dimensional Euclidean space Ån into subsets Ω1,...,ΩN by nding the coordinates of the centers τ1,...,τN of these subsets with fuzzy parameters in constraints. Real situations, which are described by models of optimal partitioning of sets, are most often characterized by a certain degree of uncertainty. In these cases, the quality of the decisions made in the optimization partitioning set problems is directly dependent on the completeness of all the uncertain factors that are signicant for the consequences of the decisions made. The class of the optimal partitioning set problem which makes it possible to consider uncertainty factors of not probabilistic-statistical nature are the optimal partitioning set problems in which either certain parameters in the model description are fuzzy, inaccurate, underdetermined or there exists an invalid mathematical description of some dependencies in the models (for example, demand functions and the cost of transporting a unit of production in innite dimensional transport problems) or the criteria themselves and (or) constraint systems are formulated inaccurately, or the optimization model admits the inuence of external uncontrolled disturbances of dierent forms and etc. The problem-solving algorithm was developed using a synthesis of methods for solving problems of the theory of optimal partitioning of sets with neuro-fuzzy technologies and modications of N.Z.Shor's r-algorithm for solving non-smooth optimization problems. The results are presented for the model problem of optimal partitioning of a set into three subsets with fuzzy parameters on constraints obtained by the developed approach. The results of the solution of the problem with the clear parameters are compared with the results when some parameters of the solved problem are fuzzy, unclear or their mathematical description is incorrect.