The Condition Evaluation of Bridges Based on Fuzzy BWM and Fuzzy Comprehensive Evaluation
Abstract
:1. Introduction
2. Fuzzy Best and Worst Method-Fuzzy Comprehensive Evaluation Model
2.1. Fuzzy Set and Membership Function
2.2. Fuzzy Best and Worst Method
Five Levels of Importance | Identically Important (II) | Slightly Important (SI) | Relatively Important (RI) | Highly Important (HI) | Extremely Important (EI) |
---|---|---|---|---|---|
CI | 3.00 | 3.8 | 5.29 | 6.69 | 8.04 |
2.3. Fuzzy Comprehensive Evaluation
3. Condition Evaluation Indicator System for Bridges
3.1. Principles for Selecting Indicators
3.2. Establishing the Indicator System
4. Case Study
4.1. Case Study 1
4.1.1. Weight Calculation for Dingjia Bridge
4.1.2. Condition Rating of Dingjia Bridge
4.2. Case Study 2
4.2.1. Weight Calculation for Jigongling Bridge
4.2.2. Condition Rating of Jigongling Bridge
5. Conclusions
- 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.
- 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.
- 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.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Five-Level Importance Scale | TFN |
---|---|
Identically Important (II) | |
Slightly Important (SI) | |
Relatively Important (RI) | |
Highly Important (HI) | |
Extremely Important (EI) |
Indicator | B1 | B2 | B3 | B4 |
---|---|---|---|---|
Best Indicator B1 | II | SI | HI | EI |
Worst Indicator B4 | EI | HI | RI | II |
Criteria Layer | Final Weights | Primary Indicator Layer | Final Weights | Set of Weights for Secondary Indicators Layer |
---|---|---|---|---|
B1 | 0.4201 | C1 | 0.3823 | {0.3152, 0.2304, 0.2478, 0.1186, 0.0787} |
C2 | 0.1793 | {0.4287, 0.3244, 0.2469} | ||
C3 | 0.2987 | {1} | ||
C4 | 0.1397 | {1} | ||
B2 | 0.3198 | C5 | 0.5510 | {0.0860, 0.0657, 0.1337, 0.2660, 0.2047, 0.2439} |
C6 | 0.2551 | {0.0878, 0.2686, 0.2171, 0.1388, 0.0707, 0.2171} | ||
C7 | 0.1939 | {0.5510, 0.2551, 0.1939} | ||
B3 | 0.1570 | C8 | 1 | {0.3452, 0.2140, 0.1125, 0.0892, 0.2392} |
B4 | 0.1032 | C9 | 0.5265 | {1} |
C10 | 0.1265 | {0.3359, 0.6642} | ||
C11 | 0.3471 | {0.2509, 0.7491} |
Criteria Layer | Primary Indicator Layer | Secondary Indicator Layer | Membership Matrix | ||||
---|---|---|---|---|---|---|---|
Excellent | Good | Fail | Poor | Critical | |||
B1 | C1 | D1 | 0 | 0.4 | 0.6 | 0 | 0 |
D2 | 0 | 0.5 | 0.5 | 0 | 0 | ||
D3 | 0 | 0.3 | 0.7 | 0 | 0 | ||
D4 | 0 | 0 | 0.4 | 0.6 | 0 | ||
D5 | 0 | 0 | 0.7 | 0.3 | 0 | ||
C2 | D7 | 0 | 0.5 | 0.5 | 0 | 0 | |
D7 | 0 | 0.4 | 0.6 | 0 | 0 | ||
D8 | 0 | 0.6 | 0.4 | 0 | 0 | ||
C3 | D9 | 0 | 0.4 | 0.6 | 0 | 0 | |
C4 | D10 | 0 | 0 | 0.7 | 0.3 | 0 | |
B2 | C5 | D11 | 0 | 0.6 | 0.4 | 0 | 0 |
D12 | 0 | 0.5 | 0.5 | 0 | 0 | ||
D13 | 0 | 0.3 | 0.7 | 0 | 0 | ||
D14 | 0.8 | 0.2 | 0 | 0 | 0 | ||
D15 | 0 | 0.7 | 0.3 | 0 | 0 | ||
D16 | 0 | 0.4 | 0.6 | 0 | 0 | ||
C6 | D13 | 0 | 0.3 | 0.7 | 0 | 0 | |
D14 | 0.8 | 0.2 | 0 | 0 | 0 | ||
D15 | 0 | 0.7 | 0.3 | 0 | 0 | ||
D16 | 0 | 0.4 | 0.6 | 0 | 0 | ||
D17 | 0 | 0 | 0.6 | 0.4 | 0 | ||
D18 | 0 | 0 | 0.5 | 0.5 | 0 | ||
C7 | D19 | 0 | 0.7 | 0.3 | 0 | 0 | |
D20 | 0 | 0.5 | 0.5 | 0 | 0 | ||
D21 | 0 | 0.6 | 0.4 | 0.6 | 0 | ||
B3 | C8 | D22 | 0.2 | 0.8 | 0 | 0 | 0 |
D23 | 0 | 0.4 | 0.6 | 0 | 0 | ||
D24 | 0 | 0.7 | 0.3 | 0 | 0 | ||
D25 | 0 | 0.6 | 0.4 | 0 | 0 | ||
D26 | 0 | 0.7 | 0.3 | 0 | 0 | ||
B4 | C9 | D27 | 0 | 0.5 | 0.5 | 0 | 0 |
C10 | D28 | 0 | 0.7 | 0.3 | 0 | 0 | |
D29 | 0.8 | 0.2 | 0 | 0 | 0 | ||
C11 | D30 | 0 | 0.8 | 0.2 | 0 | 0 | |
D31 | 0 | 0.4 | 0.6 | 0 | 0 |
Criteria Layer | Primary Indicator Layer | Optimal Weight | Comprehensive Evaluation Vector |
---|---|---|---|
B1 | C1 | 0.3823 | (0, 0.32, 0.58, 0.10, 0) |
C2 | 0.1793 | (0, 0.49, 0.51, 0, 0) | |
C3 | 0.2987 | (0, 0.40, 0.60, 0, 0) | |
C4 | 0.1397 | (0, 0, 0.70, 0.30, 0) |
Target Layer | Criteria Layer | Optimal Weight | Comprehensive Evaluation Vector |
---|---|---|---|
A | B1 | 0.4201 | (0, 0.33, 0.59, 0.08, 0) |
B2 | 0.3198 | (0.17, 0.36, 0.37, 0.10, 0) | |
B3 | 0.1570 | (0.07, 0.66, 0.27, 0, 0) | |
B4 | 0.1032 | (0.07, 0.48, 0.45, 0, 0) |
Criteria Layer | Final Weights | Primary Indicator Layer | Final Weights | Set of Weights for Secondary Indicators Layer |
---|---|---|---|---|
B1 | 0.4873 | C1 | 0.5333 | {0.4484, 0.2651, 0.1558, 0.0765, 0.0542} |
C2 | 0.2667 | {0.5714, 0.2857, 0.1429} | ||
C3 | 0.1333 | {1} | ||
C4 | 0.0667 | {1} | ||
B2 | 0.3057 | C5 | 0.5714 | {0.3716, 0.2548, 0.1740, 0.0928, 0.0634, 0.00434} |
C6 | 0.2857 | {0.3630, 0.2547, 0.1968, 0.0801, 0.0619, 0.0435} | ||
C7 | 0.1429 | {0.6338, 0.2274, 0.1388} | ||
B3 | 0.1272 | C8 | 1 | {0.3940, 0.3034, 0.1576, 0.0819, 0.0631} |
B4 | 0.00798 | C9 | 0.6338 | {1} |
C10 | 0.2274 | {0.5, 0.5} | ||
C11 | 0.1388 | {0.5, 0.5} |
Indicator | D22 | D23 | D24 | D25 | D26 |
---|---|---|---|---|---|
Best Indicator D22 | II | SI | RI | EI | RI |
Worst Indicator D25 | EI | HI | SI | II | SI |
Method | Secondary Indicators Layer | Optimal Weights | CR | Number of Comparisons |
---|---|---|---|---|
AHP | D22 | 0.3811 | 0.0625 | |
D23 | 0.2869 | |||
D24 | 0.1203 | |||
D25 | 0.0820 | |||
D26 | 0.1297 | |||
BWM | D22 | 0.4664 | 0.0608 | |
D23 | 0.2291 | |||
D24 | 0.1161 | |||
D25 | 0.0570 | |||
D26 | 0.1314 | |||
FBWM | D22 | 0.3317 | 0.0448 | |
D23 | 0.2865 | |||
D24 | 0.1437 | |||
D25 | 0.0944 | |||
D26 | 0.1437 |
Criteria Layer | Final Weights | Primary Indicator Layer | Final Weights | Set of Weights for Secondary Indicators Layer |
---|---|---|---|---|
B1 | 0.4133 | C1 | 0.3776 | {0.3034, 0.2256, 0.2783, 0.1066, 0.0861} |
C2 | 0.1852 | {0.3998, 0.3145, 0.2857} | ||
C3 | 0.3002 | {1} | ||
C4 | 0.1367 | {1} | ||
B2 | 0.3246 | C5 | 0.5498 | {0.0886, 0.0701, 0.1249, 0.2578, 0.1998, 0.2588} |
C6 | 0.2610 | {0.0902, 0.2685, 0.2208, 0.1383, 0.0711, 0.2111} | ||
C7 | 0.1892 | {0.5487, 0.2539, 0.1974} | ||
B3 | 0.1620 | C8 | 1 | {0.3317, 0.2865, 0.1437, 0.0944, 0.1437} |
B4 | 0.1001 | C9 | 0.5263 | {1} |
C10 | 0.1307 | {0.3405, 0.6595} | ||
C11 | 0.3430 | {0.2496, 0.7504} |
Criteria Layer | Primary Indicator Layer | Secondary Indicator Layer | Membership Matrix | ||||
---|---|---|---|---|---|---|---|
Excellent | Good | Fail | Poor | Critical | |||
B1 | C1 | D1 | 0 | 0.3 | 0.6 | 0 | 0 |
D2 | 0 | 0.82 | 0.5 | 0 | 0 | ||
D3 | 0 | 0.12 | 0.7 | 0 | 0 | ||
D4 | 0 | 0.5 | 0.4 | 0 | 0 | ||
D5 | 0 | 0 | 0.7 | 0.35 | 0 | ||
C2 | D7 | 0 | 0.2 | 0.5 | 0 | 0 | |
D7 | 0 | 0.16 | 0.6 | 0 | 0 | ||
D8 | 0 | 0.6 | 0.4 | 0 | 0 | ||
C3 | D9 | 0 | 0.7 | 0.6 | 0 | 0 | |
C4 | D10 | 0 | 0.1 | 0.7 | 0 | 0 | |
B2 | C5 | D11 | 0 | 0 | 0.4 | 0.25 | 0 |
D12 | 0 | 0.7 | 0.5 | 0 | 0 | ||
D13 | 0 | 0.5 | 0.7 | 0 | 0 | ||
D14 | 0.8 | 0.2 | 0 | 0 | 0 | ||
D15 | 0 | 0.7 | 0.3 | 0 | 0 | ||
D16 | 0 | 0.45 | 0.6 | 0 | 0 | ||
C6 | D13 | 0 | 0.4 | 0.7 | 0 | 0 | |
D14 | 0 | 0.8 | 0 | 0 | 0 | ||
D15 | 0 | 0.5 | 0.3 | 0 | 0 | ||
D16 | 0 | 0.6 | 0.6 | 0 | 0 | ||
D17 | 0 | 0 | 0.6 | 0.3 | 0 | ||
D18 | 0 | 0.1 | 0.5 | 0 | 0 | ||
C7 | D19 | 0 | 0.7 | 0.3 | 0 | 0 | |
D20 | 0 | 0.6 | 0.5 | 0 | 0 | ||
D21 | 0 | 0.7 | 0.4 | 0 | 0 | ||
B3 | C8 | D22 | 0 | 0.34 | 0 | 0 | 0 |
D23 | 0 | 0.25 | 0.6 | 0 | 0 | ||
D24 | 0 | 0.4 | 0.3 | 0 | 0 | ||
D25 | 0.11 | 0.85 | 0.4 | 0 | 0 | ||
D26 | 0.15 | 0.80 | 0.3 | 0 | 0 | ||
B4 | C9 | D27 | 0 | 0.4 | 0.5 | 0 | 0 |
C10 | D28 | 0 | 0.5 | 0.3 | 0 | 0 | |
D29 | 0 | 0.8 | 0 | 0 | 0 | ||
C11 | D30 | 0 | 0.3 | 0.2 | 0 | 0 | |
D31 | 0 | 0.5 | 0.6 | 0 | 0 |
Bridge Comprehensive Condition | Bridge Components | Weight | Technical Condition Rating | Technical Condition Grade | Evaluation Result |
Superstructure | 0.40 | 73.5 | 3 | Dr = 77.4 Class III bridge | |
Substructure | 0.40 | 82.0 | 2 | ||
Bridge Deck System | 0.20 | 76.0 | 3 |
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Li, Y.; Deng, J.; Wang, Y.; Liu, H.; Peng, L.; Zhang, H.; Liang, Y.; Feng, Q. The Condition Evaluation of Bridges Based on Fuzzy BWM and Fuzzy Comprehensive Evaluation. Appl. Sci. 2025, 15, 2904. https://doi.org/10.3390/app15062904
Li Y, Deng J, Wang Y, Liu H, Peng L, Zhang H, Liang Y, Feng Q. The Condition Evaluation of Bridges Based on Fuzzy BWM and Fuzzy Comprehensive Evaluation. Applied Sciences. 2025; 15(6):2904. https://doi.org/10.3390/app15062904
Chicago/Turabian StyleLi, Yunyu, Jingwen Deng, Yongsheng Wang, Hao Liu, Longfan Peng, Hepeng Zhang, Yabin Liang, and Qian Feng. 2025. "The Condition Evaluation of Bridges Based on Fuzzy BWM and Fuzzy Comprehensive Evaluation" Applied Sciences 15, no. 6: 2904. https://doi.org/10.3390/app15062904
APA StyleLi, Y., Deng, J., Wang, Y., Liu, H., Peng, L., Zhang, H., Liang, Y., & Feng, Q. (2025). The Condition Evaluation of Bridges Based on Fuzzy BWM and Fuzzy Comprehensive Evaluation. Applied Sciences, 15(6), 2904. https://doi.org/10.3390/app15062904