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Wind farms equipped by Doubly-Fed Induction Generators (DFIG) should have two capabilities so that system operators can efficiently utilizes them. These capabilities include Fault-Ride-Through (FRT) and smoothing the output active power fluctuations, especially when these generators provide significant electrical power. The Superconducting Fault Current Limiter (SFCL) and also the Superconducting Magnetic Energy Storage (SMES) are supplementary devices which are used to enhance these capabilities and reduce electrical power swings. In the present work, improvement of FRT capability and smoothing the output power of wind farms are formulated as a multi-objective problem in a fuzzy framework. The variables of optimization are the Proportional-Integral (PI) gains of DFIG and SMES controllers and also SMES and SFCL parameters. Minimization of the initial energy stored in the SMES unit, the energy losses of SFCL, deviations of the DC-link voltage of DFIG, deviations of output active power of DFIG, deviations of output voltage of DFIG, and DFIG speed deviations are six objective functions of the problem. These objective functions are scaled by a fuzzy operator, then the scaled objective functions are aggregated by the “max-geometric mean” operator to obtain the multi-objective function. For optimizing this multi-objective function, the Hybrid Big Bang Big Crunch (HBB-BC) as a meta-heuristic optimization algorithm is used. The proposed algorithm is implemented on a case study to numerically evaluate its efficiency. Simulation results show that the proposed algorithm is more effective to enhance FRT capability and smooth output power of wind farm in comparison with the other algorithms. Keywords: Doubly Fed Induction Generator (DFIG), Fault-Ride-Through (FRT), Superconducting Magnetic Energy Storage (SMES), Superconducting Fault Current Limiter (SFCL), Hybrid Big Bang Big Crunch (HBB-BC)