The Problem of Adequacy of the Analytic Hierarchy Process

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Abstract

The Analytic hierarchy process (AHP) is a popular method for solving multi-criteria problems. However, the problem of the adequacy of the AHP method is not solved. Opponents of the Analytic hierarchy process believe that the AHP as a whole is erroneous and cannot be applied in practice. Proponents of the method believe that the disadvantages of the method are compensated by a simple measurement procedure. In this paper, a modification of the AHP method is proposed. A mathematical model of measurement is formulated, which contains a built-in mechanism for checking adequacy. moreover, the measurement method is preserved, and the calculation algorithm becomes even simpler. The fact is that the Analytic hierarchy process is based on the assumption that the scale of relations can be obtained by pairwise comparison using numerical judgments based on the absolute scale of numbers. Fechner’s psychophysical law is considered as a justification for the existence of the scale of relations. But there are not one, but two psychophysical laws. The existence of two psychophysical laws is a problem of psychophysics. This problem can be solved by the rating method. To overcome the disadvantages of the Analytic hierarchy process, it is also proposed to use the rating method. The use of the rating method makes it possible to use the fundamental scale of the AHP method. As an example, the problem is solved using the traditional AHP scale.

General Information

Keywords: Fechner’s law, Stevens’ law, MAI method, hierarchy analysis method, rating

Journal rubric: Optimization Methods

DOI: https://doi.org/10.17759/mda.2020100407

For citation: Romanchuk V.M. The Problem of Adequacy of the Analytic Hierarchy Process. Modelirovanie i analiz dannikh = Modelling and Data Analysis, 2020. Vol. 10, no. 4, pp. 79–87. DOI: 10.17759/mda.2020100407. (In Russ., аbstr. in Engl.)

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Information About the Authors

Vasily M. Romanchuk, PhD in Physics and Matematics, Associate professor, Chair of “Engineering mathematics”, Belarusian national technical University, Minsk, Belarus, ORCID: https://orcid.org/0000-0001-9687-2919, e-mail: romanchak@bntu.by

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