For short-term wind power forecasting, an interval A2-C1 type-2 Takagi-Sugeno-Kang (TSK) fuzzy logic systems(IT2 A2-C1 FLS) method based on extended Kalman filter (EKF) optimization algorithm is proposed, where "A" means antecedent and "C" consequent. Compared with the type-1 FLS model, IT2 TSK FLS method can simultaneously model both intra-individual and inter-individual uncertainty, and further optimize the antecedent and consequent parameters using EKF to further improve the forecasting performance. The proposed IT2 A2-C1 FLS method is applied to Mackey-Glass chaotic time series and wind power forecasting instances in a certain region, under the same conditions, it is also compared with the type-1 TSK FLS and IT2 TSK FLS methods with the back propagation (BP) and particle swarm optimization (PSO) algorithms, as well as IT2 A2-C0 TSK FLS methods with EKF. Experimental results confirm that the proposed IT2 A2-C1 FLS method is superior to other FLS methods in performance,showing its effectiveness and application potential.