Deep reinforcement learning has achieved excellent results in many complex tasks, but its policies still lack real-time safety guarantees in dynamic, high-dimensional environments. It is therefore urgent to introduce a safety monitoring mechanism during deployment that can evaluate and correct agent decisions in real time. Existing data-driven black-box monitoring methods focus on discrete or binary decisions and are hard to transfer directly to continuous action spaces. To address the above issue, this study proposes a fuzzy-mapping-entropy-driven safety monitoring framework, which can be constructed solely from state, action, and cost data without requiring any environment model. Specifically, the method first uses a Gaussian mixture model (GMM) to perform hard partitioning of states and soft membership of actions on the offline collected safe trajectories, and proposes fuzzy mapping entropy to adaptively determine the optimal number of action clusters under the premise of balancing uniformity and model complexity. Next, fuzzy logic rules are built in the Mamdani framework, and cluster centers are jointly fine-tuned with a residual network and an adversarial discriminator to make the generated actions closer to the real safe distribution. In the online phase, the monitor computes a cluster consistency measure for each pending state-action pair based on GMM posterior probabilities. If this measure falls below a threshold, fuzzy inference is used to generate a smooth safe replacement action, thus correcting the action before a risk occurs. PPO-Lag, TRPO-Lag, and CPPO-PID policies are evaluated under the proposed monitoring framework on three navigation tasks in Safety-Gymnasium. The results show that the framework significantly reduces cumulative safety costs while keeping almost the same or slightly higher task returns and maintains a high warning coverage rate, which confirms its effectiveness and practicality in continuous action scenarios.