Hierarchy analysis process is one of the most used methods of decision-making in investment analysis, which successfully combines formalization and transparency of the procedures with the reliability of the result. In the paper the key stages of the practical issues of using the analytic hierarchy process in multi-criteria analysis of portfolio alternatives are focused. The expediency of multilevel hierarchical decomposing of comparison criteria is presented, the procedures used for quantify the consistency of pairwise comparisons are shown, the critical analysis of the scale of relative importance was made. Some controversial aspects of practical use of the analytic hierarchy process, which met with a number of organizational and mathematical difficulties, such as the inconsistency determination in matrices of pairwise comparison and reasonable simplifying of the traditional scale of relative importance were discussed. Guidelines for effective solution of the issues above using approximate calculation of eigenvectors and rationalization of the scale shown on the basis of experience of foreign researchers and the author´s analysis. Main paper´s results allow better use of the applied analytic hierarchy process and more active implement it in management practice.
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