In this article, fixed-time projective synchronization (FTPS) and predefined-time projective synchronization (PTPS) for a class of discontinuous fuzzy inertial neural networks (FINNs) with distributed delays are considered. To this end, regarding differential inclusion theories and the Lyapunov stability method, more precise and improved setting times of FTPS are systematically constructed. Furthermore, a more general and novel predefined-time stability lemma is established to make the synchronized time more flexible and can be an accurate value in advance. Meanwhile, some effective feedback controllers and new criteria are established to guarantee the proposed FINNs achieve FTPS and PTPS, respectively. Finally, the corresponding numerical simulations and image encryption application are offered to confirm the obtained results.

中文翻译：

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一类具有分布式时滞的模糊惯性不连续神经网络的固定/预定义时间射影同步

在本文中，考虑了一类具有分布式延迟的不连续模糊惯性神经网络（FINN）的固定时间投影同步（FTPS）和预定义时间投影同步（PTPS）。为此，基于微分包含理论和Lyapunov稳定性方法，系统地构建了更精确和改进的FTPS设置时间。此外，还建立了一种更通用、更新颖的预定义时间稳定性引理，使同步时间更加灵活，可以提前得到准确的值。同时，建立了一些有效的反馈控制器和新的标准来保证所提出的 FINN 分别实现 FTPS 和 PTPS。最后，提供了相应的数值模拟和图像加密应用来验证所获得的结果。