<p>This paper proposes a novel discrete-time event-triggered Takagi-Sugeno (T-S) fuzzy fractional-order observer for T-S fractional-order models subject to external disturbances in the state and output vectors. First, we design a new discrete-time event-triggered mechanism (DTETM) and a fuzzy fractional-order observer using only the knowledge of the output vector at the triggering instants of the newly proposed DTETM. Then, by employing some properties of the Caputo derivative, we establish existence conditions in terms of a convex optimization problem for the proposed discrete-time event-triggered T-S fuzzy fractional-order observer. The optimization problem provides unknown observed matrices and minimized attenuation levels. Third, we provide an effective algorithm to design the T-S fuzzy fractional-order observer. Finally, we provide numerical results and simulations to demonstrate the effectiveness of the obtained theoretical results. Unlike the existing works in the literature relating to the design of state observers for T-S fractional-order systems, where the fractional-order state observers are designed with the assumption that the information of the output vectors is not affected by disturbances, and they are only updated at each sampling instant, the one in this paper using the output vectors affected by disturbances when an event-triggered condition holds. Therefore, the method in this paper may be advantageous in saving communication resources while guaranteeing estimation performance.</p>