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This paper proposes an efficient approach for tuning L1 feedback filter of adaptive controller for multi-input multi-output (MIMO) systems. The feedback filter provides performance that trades off fast closed loop dynamics, robustness margin, and control signal range. Thus appropriate tuning of the filter's parameters is crucial to achieve optimal performance. For MIMO systems, the parameters tuning is challenging and requires a multi-objective performance indices to avoid instability. This paper proposes a fuzzy-based L1 feedback filter design tuned with multi-objective particle swarm optimization (MOPSO) to remove these bottlenecks. MOPSO guarantees the appropriate selection of the fuzzy membership functions. The proposed approach is validated using twin rotor MIMO system and simulation results demonstrate the efficacy of here proposed while preserving the system stabilizability., Comment: keywords Fuzzy logic control, multi-objective particle swarm optimization, estimate, L1 Adaptive control, fuzzy-L1 adaptive controller, Filter tuning, Fuzzy membership function tuning, pareto optimal front, optimal tuning, twin rotor MIMO system, Fuzzy membership function optimization, Robustness, Adaptation, multi-input multi-output, single-input single-output, PSO, FLC, MO-PSO