Implementation of non-linear defuzzification of linguistic indicators of preferences in the Saaty’s analytic hierarchy process

Authors

DOI:

https://doi.org/10.15587/1729-4061.2025.332092

Keywords:

hierarchy analysis method, preference levels, linguistic indicators, normalized weight coefficients

Abstract

The object of the study is the method of hierarchy analysis, as it is more widely used for solving multicriteria decision-making problems (DM). The subject is the Saaty preference level scale and methods for establishing normalized weight coefficients (NWC). The problem is to increase the accuracy of multicriteria decisions, where the linear defuzzification of linguistic preference indicators (PI), used to form pairwise comparison matrices (PCM), does not correspond to the peculiarities of human thinking. The essence of the results is that for basic IPs (IP9, IP7, IP5, IP3, IP1) NWCs are established by the mathematical method of prioritization (MPM), adapted for the needs of research, for intermediate IPs (IP8, IP6, IP4, IP2) – by multiplicative aggregation of NWCs of neighboring PIs. The peculiarity is that it is established that the application of the results of the II iteration of MoP with XII, which are nonlinear, form a step scale, and provide the proper accuracy of priority measurements, is acceptable. The quantitative indicator of sensitivity to the measurement of linguistic preferences increased by 4.5 times compared to the linear scale. However, the average quantitative indicator of the establishment of false IP in the nonlinear scale turned out to be 1.84 times higher than in the linear one. which places additional requirements on the competence of experts, as well as the need to control their attentiveness during the PCM formation.

The relative quantitative indicator corresponding to the increase in the NWC of the Saaty scale terms, formed using the modifier “very” by performing the fuzzy operation “concentration”, has increased almost twice, “double concentration” – by a third. Which is more consistent with the quantitative-qualitative logic of the relationship between the specified terms. The practical use of the obtained results will help prevent the negative phenomenon of rank reversal in multi-criteria DM problems

Author Biographies

Oleksii Reva, State Scientific Institution "Ukrainian Institute of Scientific and Technical Expertise and Information"

Doctor of Technical Scienes, Professor, Head Researcher

Volodymyr Kamyshyn, State Scientific Institution "Ukrainian Institute of Scientific and Technical Expertise and Information"

Doctor of Pedagogical Scienes, Corresponding Member of the National Academy of Educational Sciences of Ukraine

Director

Serhii Borsuk, State Scientific Institution "Ukrainian Institute of Scientific and Technical Expertise and Information"

Doctor of Technical Scienes, Associate Professor, Head Researcher

Pavlo Mamenko, Kherson State Maritime Academy

PhD, Associate Professor

Department of Ship Handling at Sea

Kostiantyn Kyrychenko, Kherson State Maritime Academy

PhD, Associate Professor

Department of Health and Safety, Professional and Applied Physical Training

Larysa Sahanovska, Flight Academy of the National Aviation University

Senior Lecturer

Department of Physical and Mathematical Disciplines and Information Technologies in Aviation Systems

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Implementation of non-linear defuzzification of linguistic indicators of preferences in the Saaty’s analytic hierarchy process

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Published

2025-06-25

How to Cite

Reva, O., Kamyshyn, V., Borsuk, S., Mamenko, P., Kyrychenko, K., & Sahanovska, L. (2025). Implementation of non-linear defuzzification of linguistic indicators of preferences in the Saaty’s analytic hierarchy process. Eastern-European Journal of Enterprise Technologies, 3(4 (135), 25–33. https://doi.org/10.15587/1729-4061.2025.332092

Issue

Vol. 3 No. 4 (135) (2025): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2025 Оleksii Reva, Volodymyr Kamyshyn, Sergii Borsuk, Pavlo Mamenko, Kostiantyn Кyrychenko, Larysa Sahanovska

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