Hierarchical Feature Evaluation and Decision‑Making for In‐Vehicle Augmented‐Reality Head‐Up Display Based on Pythagorean Hamacher Aggregation

The rapid proliferation of automotive augmented-reality head-up displays (AR-HUDs) in intelligent-driving systems has increased the need for rigorous multidimensional performance evaluation-a task complicated by data heterogeneity and cognitive uncertainty. To address this dual challenge, we propose a comprehensive decision-making method that combines Pythagorean fuzzy set and Hamacher confidence-weighted aggregation operator (PyHa-CWAO) and embeds it in a novel hierarchical evaluation framework that separately appraises the static basic information layer (SBIL) and the dynamic AR fusion layer (DAFL) before synthesizing the results. We further propose a hyperbolic tendency-confidence fused scoring model for the first time, which simultaneously captures subjective hesitation and confidence weights while amplifying interalternative discrimination. Combining DEMATEL for causal-relationship elicitation with VIKOR for multicriteria ranking yields the integrated PyHa-CWAO-DEMATEL-VIKOR decision model. A driving-simulation and eye-tracking experiment evaluated 10 AR-HUD prototypes (six DAFL, four SBIL) across 12 objective and subjective indicators. Compared with three established multicriteria decision-making methods, the proposed model improves ranking consistency by 14%, confirming its robustness and practical value. Overall, this work offers an accurate, resilient, and extensible decision tool for AR-HUD and broader extended reality interfaces, enriching fuzzy-decision theory and providing a methodological foundation for future virtual human-computer interaction optimization.