Abstract. The author obtains two solutions for the uncertainty problem in multiple decision-making for a sufficiently broad class of selection rules for preferences in a decision-making system. They are based, respectively, on the principles of guaranteed and best results, with the criteria in the form of preferences on solutions defined by explicitly given utility function, which parametrically depends on a convex statistical regularity on the set of states and on the the utility function on consequences, which is determined to within a positive linear transformation. Refs: 6 titles.

Keywords: decision-making system, uncertainty problem, multi-prior model.