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This paper is concerned with the quantized output feedback H∞ control problem for discrete-time Takagi-Sugeno fuzzy systems. The measurement output of the system is quantized by a memoryless logarithmic quantizer before being transmitted to the controller. The problem we address is the design of a full order dynamic output feedback controller ensuring the asymptotical stability and a prescribed H∞ performance level for the resulting closed-loop system. By employing a basis-dependent Lyapunov function approach, we present a sufficient condition for the solvability of the problem. Then based on this condition, several sufficient conditions for the existence of the desired controller are obtained and the expression of the controller is also given. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.