Crawler cranes operate under highly variable loads and configurations, making rapid, reliable safety assessment of boom structure essential. This study proposes a Unified Safety Index (USI) that consolidates three critical indicators: strength (maximum equivalent stress), stability (linear buckling coefficient), and stiffness (displacement) into a single quantitative score. Gaussian membership functions transform each indicator into fuzzy safety grades (“Safe”, “Warning”, “Danger”) using thresholds drawn from national and international standards. An Improved Combination Weighting method based on game theory (ICWGT) combines the Analytic Hierarchy Process and entropy weights to balance expert judgment and data dispersion, resulting in an optimized vector. The fuzzy relationship matrix and ICWGT weights are synthesized to obtain a categorical USI and a continuous score. Validation of finite-element simulations covering various configurations demonstrates accurate categorization across “Safe”, “Warning”, and “Danger” states. Sensitivity analysis, in which each weight varied by ±5%, resulted in a change of less than 3% in the score and did not alter the safety class, confirming the robustness of the proposed method.