The synthetic hierarchy method: An optimizing approach to obtaining priorities in the AHP

A new method of synthesizing local and criteria priorities into global priorities is suggested. This approach is a development of the Analytic Hierarchy Process enabling the united consideration of all horizontal and vertical connections of a hierarchical system in a single optimizing objective function based on statistical models of the synthesis process. The solution can be reduced to a linear system or to an eigenproblem of a special matrix constructed as a combination of Kronecker's sums and products of pairwise judgement matrices. A numerical example shows that the optimizing approach produces a ranking of global priorities that may be different from the ranking produced by the classical AHP.