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This paper investigates the problem of fault detection for Takagi-Sugeno (T-S) fuzzy discrete systems in finite-frequency domain. By means of the T-S fuzzy model, both a fuzzy fault detection filter system and the dynamics of filtering error generator are constructed. Two finite-frequency performance indices are introduced to measure fault sensitivity and disturbance robustness. Faults are considered in a middle frequency domain, while disturbances are considered in another certain finite-frequency domain interval. By using the generalized Kalman-Yakubovic-Popov Lemma in a local linear system model, the design methods are presented in terms of solutions to a set of linear matrix inequalities, which can be readily solved via standard numerical software. The design problem is formulated as a two-objective optimization algorithm. A numerical example is given to illustrate the effectiveness and potential of the developed techniques.