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This work aims to boost the reliability and safety of Intelligent Transportation Systems (ITSs). To meet this goal, a particular risk assessment and management scheme is introduced to provide navigation approaches with strong safety guarantees. On the one hand, the interval analysis is adopted to develop a high fidelity model used for risk assessment purposes. This model is based on a set-membership computation of the Time-To-Collision (TTC) indicator. The TTC approximation methodology, which fits well the car-following scenario, takes into account several uncertainties of distinct sources. Even more, a novel second-order set-membership TTC formalization is introduced by solving a polynomial equation with interval coefficients. This formalization is suggested in an effort to diminish modeling errors. Both the first and second order interval-based TTC are improved via a correlation analysis-based …