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In recent decades, numerous catastrophic accidents have occurred worldwide, ranging from natural events (such as tsunamis, flooding, and earthquakes) to industrial events (such as mining and chemical process disasters). They endanger humans, the environment, organizations, and societies, as well as national security. However, there have been few attempts to propose a model for assessing the required capabilities and potential challenges in crisis management system maturity (CMSM). Accordingly, this study proposes a framework for measuring CMSM levels in complex systems. To this end, a CMSM taxonomy was developed, including aspects, dimensions, and factors influencing the CMSM. Fuzzy inference sets and fuzzy analytical hierarchy processes are then used for knowledge acquisition, quantification of the CMSM, and dealing with epistemic uncertainty. An actual complex petrochemical plant is investigated to evaluate its capabilities. The findings revealed the most significant contributing factors: the CMSM’s current capability and challenges level (score), as well as the capacity to overcome the potential crisis response challenges. Moreover, the proposed model can be used as a practical approach for various chemical-processing plants.