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

Authors

  • Viktoriia Polutsyhanova National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Educational and Research Institute of Physics and Technology, information security department, Ukraine http://orcid.org/0000-0002-9729-5786
  • Serhii Smyrnov National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Educational and Research Institute of Physics and Technology, information security department, Ukraine https://orcid.org/0000-0003-4190-5204

DOI:

https://doi.org/10.20535/kpisn.2025.3.328644

Keywords:

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

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.

References

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Published

2025-09-30

Issue

Vol. 140 No. 3 (2025): KPI Science News

Section

Статті

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Copyright (c) 2025 Viktoriia Polutsyhanova, Sergii Smyrnov

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