The artificial intelligence of things (AIoT) comprises the integration of artificial intelligence (AI) technologies and the internet of things (IoT) infrastructure. The main aim of the AIoT is to design highly effective IoT operation, enhance human-machine interaction, and improve data analytics and data management. In the AIoT system, the AI is embedded into the infrastructure elements, namely programs and chipsets, which are interlinked via the IoT network. Cybersecurity in the AIoT employs AI technologies, particularly machine learning (ML), deep learning (DL), and neural networks to defend connected IoT devices, networks, and data from recent cyber threats. Since IoT devices have restricted capability, storage, and power, the AI offers intelligent and effective defenses that can learn to identify anomalies in real time. Therefore, we present a mathematically guided and explainable AI-based framework titled the mutual information-based feature ranking for detecting false data injection attacks (MIFR-DFDIA) approach in resilient distributed cybersecurity networks. The MIFR-DFDIA aims to enhance cybersecurity resilience by accurately identifying and mitigating false data injection attacks that compromise data integrity. Initially, data preprocessing was performed to handle outliers, missing values, and feature standardization for ensuring high-quality input data for analysis. Mutual information was then utilized for optimal feature selection to identify the most informative attributes effectively. For classification, a hybrid model such as a stacked variational autoencoder and a wasserstein generative adversarial network was deployed for robust and precise recognition of false data injection attacks in cybersecurity distributed systems. Finally, the explainable artificial intelligence (XAI) method based SHAP was incorporated to interpret model predictions and improve transparency in decision-making. The experimental result analysis of the MIFR-DFDIA method was carried out for a benchmark dataset, and the comparative analysis exhibited the improved solution over other techniques concerning various metrics.