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In order to control the collision of long-span cable-stayed bridges with floating systems caused by large longitudinal displacement of beam ends under earthquake action, based on the engineering background of a long-span dual-purpose double-tower cable-stayed bridge, the collision problem of the main approach bridge under earthquake action is proposed. Two kinds of intelligent fuzzy control strategies based on different membership functions are presented, using MR Damper as a control device and modeled by SIMULINK. In this paper, the damping control effect of the proposed fuzzy control strategy on the collision problem of the main approach bridge of the cable-stayed bridge is studied. The results show that changing the range of the membership function will change the size of the control current, and the longitudinal displacement and acceleration of the structure will decrease with the increase in the control current. However, when the control current is too large, the acceleration response will be amplified and oscillated. Both fuzzy controls can reduce collision times, and the peak value of collision force between the main approach bridges and the energy consumption of the MR damper are roughly similar. Based on the control effect of longitudinal displacement response, acceleration response, and collision force response of the main approach bridge and the energy consumption of the damper, fuzzy control A is better than fuzzy control B. [ABSTRACT FROM AUTHOR]