One of the main causes of accidents in safety-critical systems is human error. In order to reduce human errors in the process of handling abnormal situations that are highly complex and mentally taxing activities, operators need to be supported, from a cognitive perspective, in order to reduce their workload, stress, and the consequent error rate. Of the various cognitive activities, a correct understanding of the situation, i.e. situation awareness (SA), is a crucial factor in improving performance and reducing errors. Despite the importance of SA in decision-making in time-and safety-critical situations, the difficulty of SA modeling and assessment means that very few methods have as yet been developed. This study confronts this challenge, and develops an innovative abnormal situation modeling (ASM) method that exploits the capabilities of risk indicators, Bayesian networks and fuzzy logic systems. The risk indicators are used to identify abnormal situations, Bayesian networks are utilized to model them and a fuzzy logic system is developed to assess them. The ASM method can be used in the development of situation assessment decision support systems that underlie the achievement of SA. The performance of the ASM method is tested through a real case study at a chemical plant.