Qixiao Hu

For interval-valued intuitionistic fuzzy sets featuring complementary symmetry in evaluation relations, this paper proposes a novel, complete fuzzy multi-attribute group decision-making (MAGDM) method that optimizes both expert weights and attribute weights. First, an optimization model is constructed to determine expert weights by minimizing the cumulative difference between individual evaluations and the overall consistent evaluations derived from all experts. Second, based on the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS), the improved closeness index for evaluating each alternative is obtained. Finally, leveraging entropy theory, a concise and interpretable optimization model is established to determine the attribute weight. This weight is then incorporated into the closeness index to enable the ranking of alternatives. Integrating these features, the complete fuzzy MAGDM algorithm is formulated, effectively combining the strengths of subjective and objective weighting approaches. To conclude, the feasibility and effectiveness of the proposed method are thoroughly verified and compared through detailed examination of two real-world cases.

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.