Unlike existing memristive neural networks or fuzzy neural networks, this article investigates a class of Caputo fractional-order uncertain memristive neural networks (CFUMNNs) with fuzzy operators and transmission delay to realistically model complex environments. Especially, the fuzzy symbol AND and the fuzzy symbol OR as well as nonlinear activation behaviors are all concerned in the generalized master-slave networks. Based on the characteristics of the neural networks being studied, we have designed distinctive information feedback control protocols including three different functional sub-modules. Combining comparative theorems, inequality techniques, and stability theory, novel delay-independent conditions can be derived to ensure the finite-time synchronization (FTS) of fuzzy CFUMNNs. Besides, the upper bound of the settling time can be effectively evaluated based on feedback coefficients and control parameters, which makes the achievements of this study more practical for engineering applications such as signal encryption and secure communications. Ultimately, simulation experiments show the feasibility of the derived results.