Tyres are one of the most important safety components on a vehicle. Ignoring or failing to correctly set the tyre pressure may lead to accidents, and can affect the vehicle's fuel efficiency and tyre lifespan. Hence, there is a need for a Tyre Pressure Monitoring System (TPMS) that can effectively monitor tyre condition. The current threshold-based TPMSs are characterised by a high number of false alarms. This is mainly due to: (i) the non-static and complex relationship between tyre pressure and temperature; and, (ii) the measurement error of the pressure/temperature sensors that are used for data collection. In this paper, we propose an innovative decision rule-based approach to tyre monitoring. This approach relies on the Dominance-based Rough Set Approach (DRSA), which is a well-known multicriteria classification and preference learning method. The DRSA takes a decision table as an input and it generates a collection of if-then decision rules as an output. The complexity of pressure/temperature relationship is solved by fixing one of the parameters and then generating the decision rules based on the other parameter. The problem of false alarms is solved by a discretisation of the scale of the fixed parameter. Based on these solutions, we designed two types of analysis levels: pressure-oriented analysis and temperature-oriented analysis. The proposed approach has been validated and implemented within an important travelling company that operates in the South of England. The real-world tests showed that the proposed approach has improved the current system and has led to a substantial reduction of false alarms.