Probabilistic Simplified Neutrosophic Sets for Safety Risk Analysis of Complex System Failures under Artificial Intelligence Environment

The safety issues connected with AI-driven operations have increased in importance as AI becomes increasingly integrated into complex systems and vital infrastructure. Complex systems that depend on automated decision-making and real-time data interpretation, including smart grids, autonomous vehicles, and nuclear plant management, can have serious negative effects on people, the environment, and the economy if they malfunction. A methodical methodology for assessing safety risk elements in intricate systems functioning in AI contexts is presented in this paper. System complexity, interpretability, fault diagnostic speed, cybersecurity resilience, and vulnerability to ethical risk are among the eight main characteristics that are recognized. Ten AI-integrated application scenarios including autonomous cars and medical diagnostics are compared using a neutrosophic set methodology. We use the Probabilistic Simplified Neutrosophic Sets to overcome uncertainty information. This research suggests mitigation techniques unique to AI-specific vulnerabilities and assists in identifying the systems most at risk. For designers, operators, and legislators interested in using AI in safety-critical systems, the findings offer practical insights.