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KPI Science News
ISSN 2617-5509 · e‑ISSN 2663-7472 Open Access · CC BY 4.0
Vol. 140 · Issue 3 · 2025 Sep 30, 2025 article

METHOD FOR REFINING WEIGHTS IN MULTI-CRITERIA UTILITY FUNCTION IN MAUT

VP
Viktoriia Polutsyhanova Corresponding National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Educational and Research Institute of Physics and Technology, information security department, Ukraine Ukraine
SS
Serhii Smyrnov National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Educational and Research Institute of Physics and Technology, information security department, Ukraine Ukraine
PublishedSep 30, 2025
PDF (Ukrainian)
KPISN 3 VOL 140 · 3
VOL 140 · ISS 3 · 2025 View issue

Abstract

Background. In modern multi-criteria decision-making, a critical challenge is the determination of weight coefficients in the utility function. Classical MAUT (Multi-Attribute Utility Theory) methods often rely on subjective expert evaluations, leading to potential errors due to expert fatigue and the limited number of comparisons. Additionally, discrepancies in the total weight sum can violate the axioms of linear convolution. Objective. To develop a method for refining weight coefficients in the multi-attribute utility function of MAUT, which reduces the influence of subjectivity and ensures analytically consistent values. Methods. An approach based on the Lagrange method applied to a system of normalized weights is proposed. This method transforms relative (non-normalized) expert assessments into precise weights by solving a system of equations analytically. To minimize errors, only relative weight ratios are used, reducing the number of expert queries from quadratic to linear complexity. Results. A formula for refining weight coefficients is derived, preserving relative expert evaluations while ensuring accuracy and normalization. An example involving four criteria demonstrates the use of Lagrange multipliers to achieve refined weights with an error margin below 0.001. The method provides stable and analytically sound results without requiring complete pairwise comparisons. Conclusions. The proposed method enables efficient refinement of weight coefficients in MAUT without overburdening experts. Analytical computation reduces error risks and enhances decision-making objectivity. The method is suitable for tasks with numerous criteria and offers a robust foundation for constructing utility functions in multi-criteria models.

Keywords

#MAUT #utility function #weight coefficients #Lagrange method #expert evaluation #multi-criteria decision-making

References

  1. S. J. T. Jansen, “The Multi-attribute Utility Method”, in The Measurement and Analysis of Housing Preference and Choice. Dordrecht: Springer Neth., 2011, pp. 101–125. Accessed: Apr. 10, 2024. [Online]. Available: https://doi.org/10.1007/978-90-481-8894-9_5 .
  2. O. Bozorg-Haddad, B. Zolghadr-Asli, and H. A. Loáiciga, Handbook on Multi-Attribute Decision-Making Methods. Wiley Sons, Inc., John, 2021.
  3. H. Raiffa and R. L. Keeney, Decisions with Multiple Objectives: Preferences and Value Trade-Offs. Cambridge Univ. Press, 2014.
  4. M. Z. Zgurovsky, A. A. Pavlov, and A. S. Sh. Shtankevych, Modified method of hierarchy analysis, System Research and Information Technologies, no. 1, pp. 7–25, 2010.
  5. A.A. Pavlov, E.I. Lyschuk, V.I. Angle, Mathematical optimization models for substantiation and finding weights of objects in the pairwise comparison method, System Research and Information Technologies, no. , pp. 13–21, 2010.
  6. J. Jia, G. W. Fischer, and J. S. Dyer, “Attribute weighting methods and decision quality in the presence of response error: a simulation study”, J. Behav. Decis. Making, vol. 11, no. 2, pp. 85–105, Jun. 1998. Accessed: Apr. 10, 2025. [Online]. Available: https://doi.org/10.1002/(sici)1099-0771(199806)11:2%3C85::aid-bdm282%3E3.0.co;2-k .
  7. P. C. Fishburn and R. L. Keeney, “Generalized Utility Independence and Some Implications”, Operations Res., vol. 23, no. 5, pp. 928–940, Oct. 1975. Accessed: Apr. 10, 2025. [Online]. Available: https://doi.org/10.1287/opre.23.5.928 .
  8. P. C. Fishburn, F. K. Hwang, and H. Lee, “Do local majorities force a global majority?”, Discrete Math., vol. 61, no. 2-3, pp. 165–179, Sep. 1986. Accessed: Apr. 10, 2025. [Online]. Available: https://doi.org/10.1016/0012-365x(86)90088-9 .
  9. T. L. Saaty, “Group Decision Making and the AHP”, in The Analytic Hierarchy Process. Berlin, Heidelberg: Springer Berl. Heidelb., 1989, pp. 59–67. Accessed: Apr. 10, 2025. [Online]. Available: https://doi.org/10.1007/978-3-642-50244-6_4
  10. D. P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods. Academic Press, 1982 (reprint 2014). [Online]. Available: https://books.google.com/books/about/Constrained_Optimization_and_Lagrange_Mu.html?id=j6LiBQAAQBAJG .
  11. V. I. Polutsyhanova and S. A. Smyrnov, “Robasic method for estimating travel coefficients for MAUT,” in Inform. technologies and safety, Kiev, Ukraine, 30 sheets. 2023. Kiev: IN-T PROBLEMS OF INFORMATION REGISTRATION NAS UKRAINE, 2023, p. 50–54.
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