Road safety is one of the most significant performance indicators in traffic networks. Automation technologies can provide significant opportunities for improvement. However, evaluating the risk involved in using these technologies is not a trivial task. One of the existing tools in traffic safety evaluation are the surrogate safety metrics (SSM), which can identify conflicts and near misses. Nevertheless, existing SSMs have been mostly developed for conventional vehicles and have important disadvantages when used for the assessment of automated vehicles (AVs) or connected automated vehicles (CAVs). SSMs can be classified in critical and proactive safety metrics. Critical safety metrics such as TTC identify situations where there is an imminent danger and the response should be imminent. Proactive metrics such as DSS (Difference between Space distance and Stopping distance) identify unsafe situations where evasive action is proposed but it may not be immediately necessary. In this light, two novel SSMs for rear end collisions have been developed, based on fuzzy logic; the proactive fuzzy surrogate safety metric (PFS) and the critical fuzzy surrogate safety metric (CFS). Results of this work show that PFS and CFS are robust indicators in classifying a situation to be totally safe, certainly unsafe or even a little risky, corresponding to the spectrum of different behaviors. The proposed metrics have been tested on synthetic trajectory data and results show their robustness on evaluating the safety level in the longitudinal direction.