This study proposes an interval type-2 Tagaki-Sugeno-Kang fuzzy logic system (IT2TSKFLS) for the supervisory adaptive tracking control of robot manipulators to confront uncertainties in the robot dynamics. The IT2TSKFLS that combines interval type-2 fuzzy sets and TSK fuzzy reasoning is used to approximate unknown non-linear functions in the robot dynamics. Based on IT2TSKFLS, a supervisory controller comprises a weighed combination of the adaptive IT2TSKFLS control and the sliding-mode control (SMC) to suppress the effects of uncertainties and approximation errors. The main idea of this supervisory structure is to exploit their advantages of the IT2TSKFLS with online learning ability and the SMC with robust characteristics. Projection-type adaptive algorithms of IT2TSKFLS parameters derived from the Lyapunov synthesis approach guarantee the stability and robustness of the overall control system. The proposed approach needs no prior system information and offline learning phase. Experiments performed on a two-link robot manipulator demonstrate the effectiveness of the proposed control methodology.