<p>Most commonly employed methods for analyzing complex-valued fuzzy discontinuous inertial neural networks (CVFDINNs) necessitate the equivalent decomposition of the original system into two real-valued subsystems and calculate the second-order derivatives of the inertia term using the generalized variable substitution method, which considerably complicates the analytical process. In this paper, an overall direct analysis method and an improved predefined-time stability lemma are introduced to synchronize a class of CVFDINNs with mixed time delays, predicated on non-separation and non-reduction predefined-time control. An improved fixed-time stability lemma is derived, enabling accurate estimation of the settling time while being less conservative than classical results. Through non-smooth analysis, two control strategies are proposed to achieve predefined-time synchronization of CVFDINNs, requiring the implementation of only a single controller. The proposed approach obviates the need for multiple system conversions, streamlines the controller design and system analysis, and enhances the clarity of system synchronization outcomes. Simulation results substantiate the reliability and applicability of the proposed strategy.</p>