Interval-Valued Fermatean Quadripartitioned Neutrosophic Similarity Model for Real-Time Safety Evaluation in Electrical Automation Systems

Electrical automation systems operate in dynamic environments where sensor data are often imprecise, contradictory, or incomplete. Traditional safety evaluation approaches struggle to cope with this complexity, especially under real-time constraints. This paper introduces a novel mathematical framework based on Interval-Valued Fermatean Quadripartitioned Neutrosophic Sets (IVFQNS) for modeling and evaluating safety conditions in electrical automation systems. The proposed model captures four distinct cognitive states: truth, falsity, contradiction, and ignorance, each expressed as interval-valued degrees to reflect uncertainty more effectively. A new similarity measure tailored for IVFQNS is developed to compare the current system state with a predefined ideal safety state. The model is integrated into a structured decision-making framework suitable for real-time environments. A complete case study on an industrial automation scenario demonstrates the model’s capacity to handle uncertainty, provide quantitative safety assessment, and support timely decision-making. Results validate the model’s mathematical consistency, interpretability, and practical relevance.