In this paper, an adaptive non-singleton interval type-2 fuzzy logic controller (ANSIT2-FLC) is proposed for the flexible air-breathing hypersonic vehicle (FAHV) in order to make the velocity and altitude of the FAHV track the reference commands in a good manner when measurement noise exists in the velocity channel and altitude channel. After model linearization, a dynamic inversion controller is designed to obtain the control inputs. Then, non-singleton interval type-2 fuzzy logic system (NSIT2-FLS) is applied to deal with the measurement noise in the feedback signals as well as to approximate the uncertain terms in the dynamic inversion controller. Afterwards, adaptive laws are designed to minimize the tracking errors. Low-pass filters are further employed to filter out the high frequency noise in the output signals, while tracking differentiators (TDs) and nonlinear state observers (NSOs) are utilized to obtain the high-order derivatives of the command signals and output signals respectively. Simulations show that all the performance criteria values of ANSIT2-FLS are smaller than those of singleton IT2-FLC, which demonstrates the effectiveness of our proposed controller.