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This paper is concerned with cyberattack detection in discrete-time, leader-following, nonlinear, multi-agent systems subject to unknown but bounded (UBB) system noises. The Takagi-Sugeno (T-S) fuzzy model is employed to approximate the nonlinear systems over the true value of the state. A distributed cyberattack detection method, based on a new fuzzy set-membership filtering method, which consists of two steps, namely a prediction step and a measurement update step, is developed for each agent to identify two types of cyberattacks at the time of their occurrence. The attacks are replay attacks and false data injection attacks affecting the leader-following consensus. We calculate an estimation ellipsoid set by updating the prediction ellipsoid set with the current sensor measurement data. Two criteria are provided to detect cyberattacks based on the intersection between the ellipsoid sets. If there is no intersection between the prediction set and the estimation set of an agent at the current time instant, a cyberattack on its sensors is declared. Control signal or communication signal data of an agent are under a cyberattack if its prediction set has no intersection with the estimation set updated at the previous time instant. Recursive algorithms for solving the consensus protocol and calculating the two ellipsoid sets for detecting attacks are proposed. Simulation results are provided to demonstrate the effectiveness of the proposed method.