In recent years, vibration control of structures subjected to the wind, earthquakes and traffic loads has been broadly studied. Based on this, different types of dampers and control systems have been used and evaluated in the form of active, semi-active, passive, and hybrid control. In this study, to control the vibrations of an 11-story structure under the effect of seismic load, the semi-active control approach of structural vibrations is used, with the help of Magneto-Rheological, MR, damper and using fuzzy logic algorithm decision system. In addition to using fuzzy inference system to determine the appropriate control voltage of the MR damper, the floating fuzzy inference system is also used to improve the performance of control system. In other words, to improve the performance of the fuzzy system with fixed membership functions, floating fuzzy system has been used with variable range for membership functions. The proposed fuzzy system is implemented in two different decision states; first, making decision based on velocity and second, making decision based on the velocity and displacement. Implementation of fuzzy inference system is conducted in MATLAB, and linear and nonlinear structural model in OpenSEES, where TCP/IP connection between them is used. The results of incremental dynamic analysis with maximum acceleration of 0.1 g to 1.0 g with incremental step of 0.1 g indicate that using floating fuzzy control system for decision based on velocity reduces the average displacement of the roof about 17.6% in linear structure and 22% in nonlinear structure, while in decision making based on velocity and displacement, these values are about 1.3% and 1.34% in linear and nonlinear structures, respectively.