To select the evaluation scale in the Analytic Hierarchy Process
Abstract
To select the evaluation scale in the Analytic Hierarchy Process
Incoming article date: 27.11.2017The study of the method errors depending on the choice of numerical approximation of the linguistic variables used is proposed. It is obtained that the necessary condition for the absence of objective (independent from the opinions of experts) reasons for the inconsistency of paired comparison matrices is the closure of the numerical scale relative to the composition of estimates. . In particular, for the classical Analytic Hierarchy Process coming from the works of A. Saati, such a scale is not closed. When the criteria of one level of hierarchy are not the same in terms of priorities relative to the overlying goals (and this situation often happens), even one expert Advisor, in principle, cannot give a consistent matrix of paired ratings. What, in fact, is due to the great attention in the classical considered technology to the methods of estimating inconsistency of the matrix of paired comparisons and its minimization. As the number of experts increases, this effect increases. A closed evaluation scale can be obtained from successive degrees of one any number. For purposes of powers of a number is 1.5, although not ruled out another choice. Для таких шкал объективные причины возникновения несогласованности матицы парных сравнений отсутствуют, а субъективные, связанные с несогласованностью мнений эксперта, могут быть устранены в процессе формирования оценок. The proposed method is explained by a concrete example of the use of the hierarchy analysis method in the assessment of personnel risks in small non-commercial projects.
Keywords: Analytic Hierarchy Process, expert evaluation, evaluation scale, matrix of paired comparisons, violation of transitivity, objective reasons for inconsistency, isolation relative to the composition, AT-projects, personnel risks