Extremum in the problem of paired comparisons

Objectives. An analysis of the problem evaluating alternatives based on results expert paired comparisons is presented. The importance and relevance this task due to its numerous applications in a variety fields, whether technical natural sciences or humanities, ranging from construction politics. In such contexts, frequently arises concerning how calculate an objective ratings vector evaluations. terms mathematical formulation, finding can be reduced approximating matrices by consistent matrices. Methods. Analytical higher algebra methods are used. For some special cases, numerical calculations given. Results. theorem stating that there always unique matrix optimally approximates given inversely symmetric log-Euclidean metric proven. addition, derived formulas for calculating small dimensions, examples considered allow obtained according formula compared with other known matrix, i.e., eigenvector minimizing discrepancy log-Chebyshev metric. It proven all these lead same result dimension 3, while 4 already different. Conclusions. paper us evaluation data. This method used strategic planning cases where conclusions recommendations possible only basis