This paper investigates the adaptive interval type-2 (IT2) fuzzy dynamic memory event-triggered consensus (ETC) problem for nonlinear multi-agent systems (NMASs) under jointly connected topologies. Considering that the topologies may not always remain connected, distributed compensators are developed to estimate the leader’s states. In the design of the proposed scheme, IT2 fuzzy logic systems (FLSs) are employed to better approximate the unknown nonlinear terms. A consensus protocol incorporating a dynamic memory event-triggering mechanism (DMETM) is developed. Then, it is further shown that the proposed schemes guarantee leader-following consensus (LFC) for NMASs under jointly connected topologies while excluding the Zeno phenomenon. At last, simulations on the system of four single-link manipulators and a numerical example are performed to verify the effectiveness of the proposed consensus schemes.