FUZZY TWO-STAGE CONTINUOUS-DISCRETE PROBLEM OF OPTIMAL SET PARTITION. I. THEORETICAL FOUNDATIONS

A mathematical formulation of a fuzzy two-stage continuous-discrete optimal set partition problem is formulated, which generalizes, on the one hand, the classical finite-dimensional transport problem for the case when the production volumes at given points are unknown in advance and are found as a solution to the corresponding fuzzy continuous problem of optimal partitioning of the set of consumers (suppliers of a continuously distributed resource) into fuzzy subsets (their service areas by these points), on the other hand, discrete two-stage production-transport problems for the case of a continuously distributed resource. Theorems on the existence conditions and the type of optimal solution to the problem are proved. The developed method for its solution is based on the synthesis of the theory of optimal set partitioning and the theory of fuzzy sets. Keywords: infinite-dimensional transportation problem, two-stage, continuous problems of optimal partitioning of set from En , uncertainty, membership function, fuzziness coefficient, non-differentiable optimization.