Internet of Things (IoT) may be defined as a network of smart devices that are involved in data collection and exchange. This technology has automated the day-to-day jobs and thus made our lives easier. But, realtime analysis of data is not always possible in a typical cloud-IoT architecture, especially for latency-sensitive applications. This led to the introduction of fog computing. On one side, fog layer has the capability of data processing and computation at the network edge and thus provides faster results. But, on the other hand, it also brings the attack surface closer to the devices. This makes the sensitive data on the layer vulnerable to attacks. Thus, considering Fog-IoT security is of prime importance. The security of a system or platform depends upon multiple factors. The order of selection of these factors plays a vital role in efficient assessment of security. This makes the problem of assessment of Fog-IoT security a Multi-Criteria Decision-Making (MCDM) problem. Therefore, the authors have deployed an Interval-Valued Intuitionistic Fuzzy Set (IVIFS) based Analytical Hierarchy Process (AHP) for the said environment. Using this integrated approach, the Fog-IoT security factors and their sub-factors are prioritized and ranked. The results obtained using above hybrid approach are validated by comparing them with Fuzzy-AHP (F-AHP) and Classical-AHP (C-AHP) results and are found to statistically correlated. The ideology and results of this research will help the security practitioners in accessing the security of Fog-IoT environment effectively. Moreover, the outcome of this analysis will help in paving a path for researchers by shifting their focus towards the most prioritized factor thereby assuring security in the environment.