An Optimization Model with “Perfect Rationality” for Expert Weight Determination in MAGDM

Yuetong Liu, Chaolang Hu (), Shiquan Zhang and Qixiao Hu
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Yuetong Liu: School of Mathematics, Sichuan University, Chengdu 610065, China
Chaolang Hu: School of Mathematics, Sichuan University, Chengdu 610065, China
Shiquan Zhang: School of Mathematics, Sichuan University, Chengdu 610065, China
Qixiao Hu: School of Mathematics, Sichuan University, Chengdu 610065, China

Mathematics, 2025, vol. 13, issue 14, 1-20

Abstract: Given the evaluation data of all the experts in multi-attribute group decision making, this paper establishes an optimization model for learning and determining expert weights based on minimizing the sum of the differences between the individual evaluation and the overall consistent evaluation results. The paper proves the uniqueness of the solution of the optimization model and rigorously proves that the expert weights obtained by the model have “perfect rationality”, i.e., the weights are inversely proportional to the distance to the “overall consistent scoring point”. Based on the above characteristics, the optimization problem is further transformed into solving a system of nonlinear equations to obtain the expert weights. Finally, numerical experiments are conducted to verify the rationality of the model and the feasibility of transforming the problem into a system of nonlinear equations. Numerical experiments demonstrate that the deviation metric for the expert weights produced by our optimization model is significantly lower than that obtained under equal weighting or the entropy weight method, and it approaches zero. Within numerical tolerance, this confirms the model’s “perfect rationality”. Furthermore, the weights determined by solving the corresponding nonlinear equations coincide exactly with the optimization solution, indicating that a dedicated algorithm grounded in perfect rationality can directly solve the model.

Keywords: multi-attribute group decision making; ranking of alternatives; expert weight determination; optimization models (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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