Fuzzy Surrogate Safety Metrics for real-time assessment of rear-end collision risk. A study based on empirical observations

•Two Fuzzy Surrogate Safety Metrics (FSSMs) for rear-end collision are presented.•Unsafe situations are distinguished between critically and proactively unsafe.•The new metrics are assessed based on test track experiments.•FSSMs outperform traditional metrics based on crisps thresholds.•FSSMs are suitable for supporting driving assistance and automation systems.