Science, Technologies, Innovations №2(34) 2025, 69-76 р

http://doi.org/10.35668/2520-6524-2025-2-08

Reva O. M. — D. Sc. in Engineering, Full Professor, Head researcher, State scientific institution “Ukrainian Institute of Scientific and Technical Expertise and Information”, 180, Antonovycha Str., Kyiv, Ukraine, 03150; +38 (044) 521-00-10; ran54@meta.ua; ORCID: 0000-0002-5954-290X

Kamyshyn V. V. — D. Sc. in Pedagogy, Corresponding Member of the NAES of Ukraine, Director of State scientific institution “Ukrainian Institute of Scientific and Technical Expertise and Information”, 180, Antonovycha Str., Kyiv, Ukraine, 03150; +38 (044) 521-00-10; kvv@ukrintei.ua; ORCID: 0000-0002-8832-9470

Borsuk S. P. — D. Sc. in Engineering, Associate Professor, Head Researcher, State scientific institution “Ukrainian Institute of Scientific and Technical Expertise and Information”, 180, Antonovycha Str., Kyiv, Ukraine, 03150; greyone.ff@gmail.com; ORCID: 0000-0002-7034-7857

Mamenko P. P. — PhD in Engineering, Senior Asociate Professor of the Department of Ship Handling at Sea, Kherson State Maritime Academy, 20, Independence Ave., Kherson, Ukraine, 73000; +38 (0552) 49-54-73; pavlo.mamenko@gmail.com; ORCID: 0000-0002-0974-6904

Кyrychenko K. V. — PhD in Engineering, Senior Asociate Professor of the Department of Health and Safety, Professional and Applied Physical Training, Kherson State Maritime Academy, 20, Independence Ave., Kherson, Ukraine, 73000; +38 (0552) 49-54-73; kvklecturer@gmail.com; ORCID: 0000-0002-0974-6904

Sahanovska L. A. — Senior Lecturer of the Department of Physical and Mathematical Disciplines and Information Technologies in Aviation Systems of the Flight Academy of the National Aviation University, 1, Stepan Choban Str., Kropyvnytskyi, Kirovohrad region, Ukraine, 25005; lora-sag@ukr.net; ORCID: 0000-0002-2560-4383

REFINEMENT OF NON-LINEAR QUANTITATIVE ESTIMATES OF THE SAATI SCALE ADVANTAGES INDICATORS

Abstract. Any effective management is accompanied by a solution multi-criteria decision-making problem (MCDMP). Among the relevant methods and technologies, the Analytic Hierarchy Process has been the leading efficiency for several decades (AHP), developed by T. L. Saaty. The implementation of AHP consists in determining local vectors of priorities — normalized weight coefficients (NWC) — at all levels of the hierarchy of the MCDMP being solved. Their further synthesis leads to a global vector — integrative assessments of the studied alternatives, which and only which have the systemic property of emergence, which facilitates a thorough choice of the best of them.
Despite the positive results of numerous studies on the application and improvement of AHP, the need to construct a pairwise comparison matrix (PCM) remains unchanged, the solution of which actually leads to obtaining the desired priorities-NWC. The specified PCM is built based on direct and inverse linear score estimates-quantitative equivalents of linguistic inducers of preference (IP). Which is actually an artificial replacement of measurements in the scoring ranking scale with measurements in the interval scale. Therefore, the corresponding solutions are not optimal, because linearity is not a property of human thinking and orientation on it can lead to erroneous results.
The ranking of linguistic IRs of the Saaty scale is obvious, therefore, using the mathematical method of prioritization (MoP), known in systems analysis as the “leader problem”, nonlinear NWCs of all nine IPs, measured already in an absolute scale unique in qualimetric properties, were obtained. The acceptability for research of the results of the second iteration of the MoP is justified. The analytical description of the indicated nonlinearity was carried out in a step scale. It was established that the nonlinearity itself increased the sensitivity of the scale to the measurement of priority by 16.5 times. Quantitative estimates of the ratio of linguistic IPs associated with the modifier “very” improved in relation to the indicators of the linear scale: by 20 % for the ratio IP7–IP6, and by 17 % and 39 % for the ratio IP8–IP7 and IP8–IP6, respectively. This indicates a greater harmonization of the quantitative and qualitative adequacy of the Saaty’s scale.

Keywords: decision making, analytic hierarchy process, Saaty’s scale, non-linearity dephasification of llinguistic indicators of preference, normalized weight coefficient.

REFERENCES

  1.  Saaty, T. L., & Vargas G. (2012). Models, Methods, Concepts & Application of the Analytic Hierarhy Process. New York. Secjnd Edition. Springer Science + Bisiness Media, DOI: 10.1007/978-1-4614-3597-6.
  2. Taherdoost, H., & Madanchian, M. (2023). Multi-Criteria Decision Making (MCDM) Methods and Concepts. Encyclopedia, 3 (1). 77-87. DOI:3390/encyclopedia3010006.
  3. Reva, O. M., Kamyshyn, V. V., Borsuk, S. P., Yarotskyi, S. V., & Sahanovska, L. A. (2023). Metodolohiia systemno-informatsiinoi kvalimetrii investytsiinoi pryvablyvosti obiektiv ekspertyzy [Methodology of system-information qualimetry of investment attractiveness of objects of expertise]. Kyiv, 150 p. [in Ukr.].
  4. Sahoo, S. K., & Goswami, S. S. (2023). A Comprehensive Review of Multiple Criteria Decision-Making (MCDM) Methods: Advancements, Applications, and Future Directions. Decision Making Advances, 1 (1), 25-48. DOI: 31181/dma1120237.
  5. Hrynchak, N. A. (2023). Kontseptualni aspekty bahatokryterialnoho pryiniattia rishen v upravlinskii diialnosti [Conceptual aspects of multi-criteria decision-making in management activities]. Naukovyi visnyk Natsionalnoi akademii statystyky, obliku ta audytu [Scientific Bulletin of the National Academy of Statistics, Accounting and Auditing], 1-2, 68-76. DOI: 10.31767/nasoa.1-2-2023.07. [in Ukr.].
  6. Sałabun, W. (2015). The Characteristic Objects Method: A New Distance-based Approach to Multicriteria Decision-making Problems. Journal of Multi-Criteria Decision Analysis, 22 (1-2), 37-50.
  7. Weistroffer, R., & Li, Y. (2016). Multiple criteria decision analysis software. Ch 29 in: Greco, S, Ehrgott, M and Figueira, J, eds. Multiple Criteria Decision Analysis: State of the Art Surveys Series, Springer: New York, P. 1301-1341. Retrieved from: https://link.springer.com/chapter/10.1007/97.8-1-4939-3094-4_29?fromPaywallRec=true.
  8. Amoyal, J. (2018). Decision analysis : Biennial survey demonstrates continuous advancement of vital tools for decision-makers, managers and analysts. OR/MS Today. DOI:1287/orms.2018.05.13.
  9. Mahmoudi, A., Javed, S. A., & Mardani, A. (16 March 2021). Gresilient supplier selection through Fuzzy Ordinal Priority Approach: decision-making in post-COVID era. Operations Management Research, 15(1–2), 208- DOI:10.1007/s12063-021-00178-z.
  10. Saaty, T. L. (2008). The analytic hierarchy and analytic network processes: Applications to decisions under risk. European Journal of Pure and Applied Mathematics, 1 (1), 122-196.
  11. Bliumberh, V. A., & Hlushchenko, V. F. (1982). Kakoe reshenye luchshe? Metod rasstanovky pryorytetov [What is the best solution: Method. priority setting]. Leningrad, 160 p. [in Russ.].
  12. Reva, O., Kamyshyn, V., Borsuk, S., Shulgin,, & Nevynitsyn, A. (2021). Qualitative Indexes of Air Traffic Controllers Attitude Toward Mistakes Hazard. Advances in Human Factors and Ergonomics 2021: 12th International Conference on Applied Human Factors and Ergonomics and the Affiliated Conferences (AHFE 2021), July, 25-29, Florida, USA, Springer, P. 618-624.
  13. Reva, O., Kamyshyn, V., Borsuk, S., & Nevynitsyn, A. (2022). α-Method of Air Traffic Controllers’ Preference System Specification Over Typical Mistakes Severities. ICT with Intelligent Ap-plications. Smart Innovation, Systems and Technologies, 248. Springer, Singapore. DOI: https://doi.org/10.1007/978-981-16-4177-0_68.