This paper studies the current sharing and voltage balancing problems of direct current microgrids (DC-MGs) consisting of distributed generation units (DGUs) connected by a communication network. The main challenge is that the DC-MG model is prone to unknown dynamic models and external disturbances. Moreover, the voltage at each DGU's point of coupling (PC) has to converge to its desired value while the information of the DGU filter current is exchanged with the nearest neighbors. To this end, the suggested distributed control algorithm benefits from an interval type-3 fuzzy logic system (IT3FLS). To enhance the accuracy of the approximation, a learning strategy is designed based on a correntropy unscented Kalman filter (CUKF) with a fuzzy kernel size. Utilizing the approximation technique and merging the consensus-based secondary control policy with the proposed type-3 fuzzy (T3F) controller result in the balanced voltages of the closed-loop DC-MG. The convergence of the trajectories of the DC-MG is ensured and the effects of approximation error signals are investigated via the proposed method. Furthermore, the robustness of the voltages and currents against unknown uncertainties admits the efficiency of the suggested learning-based control policy. The simulation results also confirm the appropriate transient response and the robustness of trajectories, thus the suggested controller can be implemented for practical cases.