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This paper is concerned with the problem of asynchronous H ∞ filtering for a class of discrete-time Takagi-Sugeno fuzzy affine systems against time-varying signal transmission delays and measurement quantization. The asynchrony refers to the situation that the plant state and the filter state belong to different local state space regions, and the quantization density can be adjusted to satisfy different performance requirements at different time instants. By transforming the filtering error system into an input-output form consisting of two interconnected subsystems, sufficient conditions on the existence of the desired asynchronous filter are established via the scaled small gain theorem to ensure that the closed-loop system is asymptotically stable with a prescribed H ∞ performance index with the aid of a novel piecewise Lyapunov-Krasovskii functional and the S -procedure approach. Finally, a practical example of cart-pendulum with a modified model is provided to illustrate the effectiveness of the obtained theoretical results.