Detecting misbehavior in vehicular ad-hoc networks is very important problem with wide range of implications including safety related and congestion avoidance applications. Most misbehavior detection schemes are concerned with detection of malicious nodes. In most situations, vehicles would send wrong information because of selfish reasons of their owners. Because of rational behavior, it is more important to detect false information than to identify misbehaving nodes. In this paper, we propose the variable precision rough sets based misbehavior detection scheme which detects false alert message and misbehaving nodes by observing their action after sending out the alert messages. In the proposed scheme, the alert information system, alert profile is constructed from valid actions of moving nodes in vehicular ad-hoc networks. Once a moving vehicle receives an alert message from another vehicle, it finds out the alert type from the alert message. When the vehicle later receives a beacon from alert raised vehicle after an elapse of time, then it computes the relative classification error by using variable precision rough sets from the alert information system. If the relative classification error is lager than the maximum allowable relative classification error of the alert type, the vehicle decides the message as false alert message. Th performance of the proposed scheme is evaluated as two metrics: correct ratio and incorrect ratio through a simulation.