This article delves into quasi-projective synchronization (Q-PS) problem for a class of discrete-time fractional-order T-S fuzzy complex-valued neural networks (DFTSFCNNs) with leakage and time-varying delays. First of all, according to the theory of discrete fractional calculus and properties of Mittag-Leffler function, an innovative property of discrete Mittag-Leffler function is strictly proved, and then an inequality for dealing with mixed time delays is rigorously derived. Next, by utilizing Caputo fractional difference theory and combining with property and the inequality offered in this article, some easily verifiable Q-PS criteria are derived under complex-valued fuzzy linear controller. Eventually, a numerical example is presented to demonstrate availability of the derived results.

In this paper, we study cellular neural networks with almost periodic variable coefficients and time-varying delays. By using the existence theorem of almost periodic solution for general functional differential equations, introducing many real parameters and applying the Lyapunov functional method and the technique of Young inequality, we obtain some sufficient conditions to ensure the existence, uniqueness, and global exponential stability of almost periodic solution. The results obtained in this paper are new, useful, and extend and improve the existing ones in previous literature.