Fog computing technology has gained significant attention among Internet users to establish an efficient connection between the Internet of Things (IoT) devices and cloud data centers. The characteristics of the fog computing encounter the different security challenges over the fog nodes or end-users. With the increased type of attacks in the fog platform such as port scanning attack, denial-of-service attack, flooding attack, and man-in-the-middle attack, Intrusion Detection System (IDS) becomes a significant solution. Traditional IDS techniques are inefficient for the dynamic as well as light-weight fog environment. Hence, deploying the IDS techniques in the fog layer is essential to monitor and analyze the access control policies, user information, log files, and so on. Applying traditional machine learning algorithms fail to cope up with the new classes of the attacks or malicious behaviors with the reduced computational effort. Hence, adopting the incremental learning algorithm plays a significant role in modeling the dynamic security mechanism for the ever-changing fog environment. Incremental learning can learn and detect attacks or malicious behaviors in the new classes. Thus, the incremental learning based IDS is essential for detecting as well as preventing the malicious behaviors in the fog with the increased quality and the reduced storage of the training data.