# The Condition Evaluation of Bridges Based on Fuzzy BWM and Fuzzy Comprehensive Evaluation
## 1 Introduction  
A variety of factors, including loading, environmental conditions, and material degradation, contribute to the progressive decline in bridge performance throughout its service life, posing significant risks to structural safety and durability [1]. To mitigate catastrophic failures and socioeconomic losses caused by structural damage [2, 3], the implementation of scientifically rigorous evaluation models has become imperative. Such models must not only diagnose current conditions but also inform targeted maintenance strategies to extend service life and ensure safety. Bridge evaluation has long been a focal point in bridge engineering, with evolving methodologies reflecting advancements in the field. Traditional evaluation techniques, while foundational, increasingly integrate modern approaches such as Artificial Neural Networks [4], and ensemble learning techniques such as Random Forest [5], which have demonstrated remarkable predictive capabilities in controlled environments. However, their practical implementation faces insurmountable barriers in real-world bridge management scenarios. These limitations primarily stem from the prohibitive costs of large-scale sensor deployment [6], the computational complexity of model training, and the chronic data scarcity characterizing small to medium-span bridges that form the backbone of regional transportation systems [7]. Within this context, multi-criteria decision-making (MCDM) paradigms have emerged as vital tools for reconciling quantitative data limitations with expert engineering judgment. Conventional approaches such as the Analytic Hierarchy Process (AHP) [8], Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) [9], and Cloud Model [10]. Among these methods, the AHP is particularly noteworthy for its capacity to represent complex issues in structured hierarchical formats [11]. Nevertheless, AHP's requirement for \(n(n-1)/2\) pairwise comparisons in n-dimensional problems introduces exponential complexity in bridge systems with multiple interdependent criteria, frequently resulting in inconsistent priority rankings that undermine evaluation reliability [12]. The Best-Worst Method (BWM), introduced by [PERSON] [13] as a streamlined alternative, reduces comparison requirements to 2(\(n-1\)) while maintaining robust consistency ratios, as evidenced in seismic resilience evaluations of coastal bridges and lifecycle evaluations of aging infrastructure [14]. However, the conventional BWM, which relies on crisp numerical scales, fails to adequately address the linguistic ambiguities and epistemic uncertainties inherent in expert judgments. This limitation becomes particularly significant in the context of emerging measurement technologies, which often generate fuzzy data and require probabilistic risk modeling for accurate interpretation [15]. The integration of fuzzy set theory with MCDM methodologies has catalyzed significant advancements in uncertainty quantification, particularly through the Fuzzy Best-Worst Method (FBWM) employing triangular fuzzy numbers (TFNs) to model human cognitive ambiguity [16; 17]. [PERSON] et al. [18] pioneered the FBWM-TOPSIS hybrid model for critical feeder identification in power distribution networks, achieving a significant improvement in prioritization accuracy compared to conventional BWM through optimized fuzzy reference comparisons. Their work demonstrated the method's capacity to handle conflicting expert opinions with a consistency ratio significantly below the 0.1 acceptability threshold. [PERSON] et al. [19] developed an innovative FBWM-Fuzzy Cognitive Mapping (FCM) framework for construction safety management, systematically quantifying multiple risk factors through expert surveys and reducing subjective bias through iterative cognitive map refinement. [PERSON] et al. [20] further extended FBWM's applicability to supply chain blockchain readiness evaluation, achieving an exceptional consistency ratio through probabilistic fuzzy scaling of 22 blockchain adoption indicators. [PERSON] et al.