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In this paper, a class of multi-extremal stochastic programming problems is considered. Direct and dual problems are also included in this problem, respectively, in this paper the question of the existence of solutions to such problems is studied, the necessary theorems and proofs are given. Decision making under uncertainty is based on the fact that the probabilities of various scenarios are unknown. Decision-making under risk conditions is based on the fact that each situation of the development of events can be...

The decision making theory finds its application literally at any field of science, especially at geosciences, because working with natural resources requires the most accurate tools. This paper considers one question of the given theory, which is called the solution priority problem. The priority problem in multi-object optimization is quite complex, many authors understand it in their own way. Perhaps this is because now the theory of multi-purpose optimization is in its infancy: there is no holistic understandi...