In this article we put forward the concept of extracting information about the gravity anomaly sources, at which the interpretation result is assumed not one optimal solution, but a set of locally optimal solutions of the inverse gravity problem. Such decisions may be considered as a kind of singular points of the set of feasible solutions of interpretation. Therefore, this article deals with a new class of algorithms for solving inverse problems of gravity. Choosing the best solution from the set of admissible variants of interpretation is based on optimality criteria, which are borrowed from decision theory. In the paper are given the numerical calculations results, where during the formation of the set of feasible solutions using method of mounting by V.N. Strakhov.