Journal Article

A Robust Dynamic Multi-Criteria Evaluation Method Using Sampling and Density-Weighted Aggregation

Zhang, Danning, Zhan, Qiushi, Zhao, Baoyu, Yu, Haiting

2026

Overview

Dynamic multi-criteria evaluation plays a central role in assessing complex systems based on panel data. However, existing objective weighting methods often suffer from sensitivity to extreme observations and may produce unstable or even negative weights, limiting their reliability in practice. To address these issues, this study proposes an improved dynamic weighting approach by integrating sampling-based resampling with a density-weighted aggregation (DWA) scheme. The proposed method extends the traditional Vertical–Horizontal Scatter Degree (VHSD) framework by stabilizing weight estimation across repeated samples and aggregating weights in a distribution-aware manner. This design effectively reduces the influence of extreme observations and ensures non-negative and consistent weighting results. An empirical analysis based on panel data is conducted to evaluate the performance of the proposed method. The results show that, compared with the classical VHSD, the proposed approach consistently eliminates negative weights, achieves higher stability across different sampling schemes, and demonstrates improved robustness under data perturbations. In addition, the method exhibits greater sensitivity to structural variations in the data while maintaining overall consistency in evaluation outcomes. Overall, the proposed framework provides a transparent and reproducible approach for composite indicator construction and dynamic multi-criteria evaluation, and is particularly suitable for applications involving complex and heterogeneous datasets.

• Publisher: MDPI AG
• Subject: Analysis / Complex systems / Decision making / Density / Empirical analysis / Linguistics / Methods / Multiple criterion / Objectivity / Performance evaluation / Resampling / Sampling / Sensitivity / Specific gravity / Time series / Weighting methods