Internet-enabled devices are deployed by individuals for almost every task. The concept of cloud computing has proven to be beneficial for users as the processing, storage and analysis of data are performed at the cloud level. However, in the case of latency-sensitive applications, the notion is called-off as the overall response time is high. In this situation, fog computing outperforms the cloud. With fog computing, the necessary computations are performed at the edge of the network, and thus, latency is highly reduced. In parallel, the increase in smart devices around the globe has led to a considerable increase in sensitive user data across the Web, which needs to be secured. Furthermore, multidimensional security depends on various factors whose prioritization plays an important role in addressing security issues. In this context, the authors identify various fog computing security factors and their corresponding subfactors. The identified factors are evaluated for their impact on security at the fog level through the neutrosophic-analytical hierarchy process. Moreover, to corroborate the effectiveness of the proposed technique, the results obtained are compared to the results from conventional approaches such as Fuzzy-AHP and Classical-AHP and are found to be statistically correlated. The proposed mechanism can be used by security practitioners to systematically manage fog computing security factors.