The Usage of Web Services for Consistency Improvement in Pairwise Comparison Matrixes



Paired comparisons of criteria and alternatives are widely used in a large number of technical and scientific problems of the present, in which it is necessary to rank a finite set of objects or to evaluate an object. Paired comparisons are understandable and simple for an expert, they are a high-quality and reliable way of rating, however, it is known that the complexity and dimension of the criteria space in many problems leads to a high load on the expert, as a result of which incorrect or erroneous situations may arise when compiling matrixes of paired comparisons leading to a decrease in the coherence of judgments, and, as a consequence, to the adoption of irrational decisions. Algorithmic software to increase the consistency of judgments is in demand among experts and researchers, which, together with a large number of diverse tasks, creates requirements for the development of appropriate software: the ability to access a large number of users and independence from the subject area, which are highly satisfied by the web interface. In this paper, the authors describe an effective method for increasing the consistency of judgments in matrixes of pairwise comparisons. The main objective of the method is to maximize the consistency of judgments with a minimum of changes made to the matrix proposed by the expert as initial estimates. As a quantitative measure of consistency of judgments, a classic indicator is used – the index of consistency. Based on the created algorithm, the authors developed software that is available to researchers in distributed web services to support decision-making

General Information

Keywords: paired comparisons, consistency index, increased consistency, decision support, web services

Journal rubric: Data Analysis

Article type: scientific article


Funding. This research was supported by RFBR № 18–01–00382а.

For citation: Kurennykh A.E., Sudakov V.A., Osipov V.P. The Usage of Web Services for Consistency Improvement in Pairwise Comparison Matrixes. Modelirovanie i analiz dannikh = Modelling and Data Analysis, 2019. Vol. 9, no. 4, pp. 80–87. DOI: 10.17759/mda.2019090406. (In Russ., аbstr. in Engl.)


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Information About the Authors

Alexey E. Kurennykh, Graduate Student, Moscow Aviation Institute (National Research University), Moscow, Russia, e-mail:

Vladimir A. Sudakov, Doctor of Engineering, Professor of Department 805, Moscow Aviation Institute (MAI), Leading Researcher, Keldysh Institute of Applied Mathematics (Russian Academy of Sciences), Moscow, Russia, ORCID:, e-mail:

Vladimir P. Osipov, PhD in Engineering, Leading Researcher, Institute of Applied Mathematics RAS, leading researcher, Plekhanov Russian University of Economics, Moscow, Russia, e-mail:



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