This article investigates the distributed fuzzy H ∞ filtering problem for a class of Takagi-Sugeno (T-S) fuzzy model-based nonlinear systems interconnected over an undirected graph. The system we consider consists of numbers of heterogeneous nonlinear sub-units interconnected over an undirected graph by sensing, computing, and communicating with each other. First, the system is represented by an undirected graph, a T-S fuzzy model-based state-space equation of each subsystem and an interconnection condition. Based on this model, the concepts of the well-posedness, stability, and contractiveness for the class of systems are introduced, and the distributed fuzzy filtering problem is established. By applying membership-dependent multi-Lyapunov functions, a sufficient condition on the well-posedness, stability, and contractiveness of the open-loop plant is then derived in terms of linear matrix inequalities (LMIs). And then, a distributed fuzzy filter inheriting the interconnected structure of the plant is designed such that the filtering error system is contractive, and a sufficient condition is correspondingly given to obtain the desired fuzzy filter parameters by solving a set of LMIs. Finally, a numerical simulation is exploited to show the validity of the proposed design method.