In this paper, a novel performance-based fault detection and identification (FDI) strategy for turbofan gas turbine engines is proposed based on a first-order Takagi-Sugeno-Kang (TSK) fuzzy inference system. To deal with the problem of ambient condition changes, we use parameter correction to preprocess the raw measurement data, which can reduce the complexity of the FDI system. Also, the power level angle is set to be a scheduling parameter to reduce the rule number of the TSK-based FDI system. The data used to design, train, and test for the proposed FDI strategy are generated using a component-level turbofan engine model. The antecedent and consequent parameters of the proposed TSK-based FDI system are optimized using particle swarm optimization algorithm and ridge regression method. Then a robust structure against measurement biases is proposed by combining a special fuzzy inference system with the TSK-based FDI system. The performances of the first-order TSK-based FDI system and the robust FDI structure are evaluated through comprehensive simulation studies. The comparative studies confirm the superiority of the first-order TSK-based FDI system in terms of accuracy on fault detection, isolation, and identification. The robust structure has a 2%-8% improvement under relatively large measurement bias conditions in terms of successful rate index, which is demonstrated to have excellent robustness against measurement biases. Accuracy against a large scale of bias values and the computation time have been shown through comprehensive case simulations, which indicates that our proposed robust structure has desirable online performance.