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• An equivalent damping ratio is proposed to characterize the TMD contribution. • A probability of failure in the TMD control of the VIV in bridges is formulated. • Three typical TMDs for the VIV mitigation are compared. This paper investigates the parameter determination of the tuned mass damper (TMD) for mitigating the vortex-induced vibration (VIV) in bridges. At present, there is no consensus on design formulas for the TMD in the VIV mitigation. An equivalent damping ratio is proposed to characterize the TMD contribution to the VIV mitigation based on a semi-empirical nonlinear model. The effects of the uncertainties in aerodynamic parameters and structural parameters on the control effect of the TMD are studied. Three typical design formulas for the TMD are compared from the perspective of the effectiveness, robustness, and reliability. The results show that the equivalent damping ratio depends only on the TMD parameters and is sensitive to the uncertainty in the stiffness of the bridge. The vortex-induced amplitude at lock-in is moderate to the uncertainties in aerodynamic parameters. The design formulas for the free-vibration suppression are the most robust option that avoids a high probability of failure, which are recommended for the TMD mitigating the VIV in bridges. At last, a numerical example of the deep-water non-navigable bridge of the Hong Kong-Zhuhai-Macao Bridge is performed to confirm the rationality of the suggested design formulas. [ABSTRACT FROM AUTHOR]