# The Condition Evaluation of Bridges Based on Fuzzy BWM and Fuzzy Comprehensive Evaluation
## 5 Conclusions  
1. Model Introduction and Comparative Analysis: This study presents a novel integrated evaluation model that synergistically combines the FBWM and FCE methods to address uncertainties and enhance operational efficiency in bridge condition evaluation. The proposed FBWM-FCE model firstly establishes a four-layer indicator system, ensuring the system's alignment with the structural characteristics of bridges and regulatory requirements. Subsequently, by introducing TFNs to quantify linguistic ambiguities in the bridge's expert judgments, the model reduces cognitive bias compared to the conventional BWM, achieving a _CR_ of 19.7%, which is 22% lower than BWM and AHP, respectively. This innovation streamlines decision-making, requiring 20% fewer pairwise comparisons than AHP while maintaining robust methodological consistency. 2. Case Validation: The practical efficacy of the FBWM-FCE model was validated through case studies of Ding Jia Bridge and Jigongling Bridge in Hubei Province, China. Evaluations of both bridges according to the FBWM-FCE demonstrated full alignment with on-site inspections documented in _the 2020 Bridge Inspection and Evaluation Report_ issued by the Highway Administration of Hubei Provincial Department of Transportation. The model's reliability was further corroborated by its consistent outcomes with conventional standardized methods, while overcoming their limitations in procedural complexity and operational inefficiency. 3. Practical Application Significance, Limitations, and Future: A distinctive contribution of this research lies in its pioneering application of FBWM to bridge condition evaluation. The hybrid methodology reduces reliance on rigid numerical scales, decreasing subjective bias in weight determination processes, particularly in handling ambiguous expert judgments and multi-criteria interactions. Furthermore, the developed indicator system demonstrated exceptional adaptability to diverse bridge typologies, particularly small-to-medium span structures, as evidenced by its successful implementation in the Hubei Provincial Highway Bridge maintenance project. However, the current research on the real-time monitoring of bridge condition and the evaluation of long-span bridges is still not sufficient, and improvements can be made to the following aspects in the future: extending the model to long-span bridges, incorporating real-time sensor data for dynamic condition monitoring, and developing AI-driven automation for large-scale network-level evaluations. These advancements promote the proposed methodology as a transformative solution for modern infrastructure management while balancing theoretical innovation with engineering pragmatism. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Bridge** \\ **Comprehensive** \\ **Condition** \\ \end{tabular} } & \multirow{2}{*}{**Bridge Components**} & \multirow{2}{*}{**Weight**} & \multicolumn{2}{c}{**Technical Condition**} & \multicolumn{1}{c}{**Technical Condition**} & \multirow{2}{*}{**Evaluation Result**} \\  & & & **Rating** & & **Grade** & \\ \hline \hline \end{tabular}
\end{table} 
Table 13: The inspection and evaluation results for Jigingling Bridge. **Author Contributions:** Conceptualization, J.D. and Y.L. ([PERSON]); formal analysis, J.D. and H.Z. ; methodology, J.D. and Q.F. ; resources, Y.W., H.L. and L.P.; writing--original draft preparation, J.D. and Y.L. ([PERSON]); writing--review and editing, Y.L. ([PERSON]) and Q.F. ; investigation, Y.W., H.L. and L.P.; funding acquisition, Y.W., H.L. and L.P.; data curation H.Z. and J.D. All authors have read and agreed to the published version of the manuscript.