Despite the many services and virtually infinite resources offered by cloud computing such as virtual reality and intelligent building surveillance, it still faces many problems when intervening several smart objects and devices in human's life. These problems are low latency, mobility and location awareness. For solving these problems of cloud computing, the fog and mobile edge computing have been introduced. The fog and mobile edge computing (FMEC) make services and resources close to users via moving from cloud data centers to the edge of the network. The dependability of FMEC depends on supplying centric services to users. The FMEC considered as a perfect paradigm to the above-mentioned purpose due to their ability to implement the ponderous real time applications directly at the network edge via billions of linked mobile devices. The FMEC faces some challenges as in any novel technology. These challenges are security (network security, data security, privacy of usage, data storage security, etc.) and administrative policies concerns. The critical problem which prohibit the development of FMEC is how to address dynamic varying of security services with the requirements of mobile's users. For handling this problem, we sought to provide a method for selecting the proper security service which is a multi-criteria decision making (MCDM) problem. In this research, we provide a neutrosophic PROMETHEE (preference ranking organization method for enrichment evaluation) technique for multi-criteria decision making problems to describe fuzzy information efficiently. For assessing the proposed methodology we applied it to a real case study to select proper security service for FMEC in the presence of fuzzy information.