Expanding the possibilities of the metric approach based on the theory of means and the theory of errors

It is proposed to expand the capabilities of the metric approach for solving special problems, for example, in scheduling theory, by weakening the requirements for the metric axioms or by introducing probability proximity measures. The author’s results are considered at the junction of the theory of means and the research area dealing with expert error indicators set axiomatically. The result obtained by Academician A.N. Kolmogorov when he considered a system of axioms for deriving an analytical formula for the associative mean is strengthened.