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Fog and mobile-edge computing (FMEC) is a sustainable and innovative mobile networking framework that enables the offloading of cloud services and resources at the edge of mobile cellular networks to provide high bandwidth and ultra-low latency. Nonetheless, how to handle several dynamically varying security services with the mobile user's requirements efficiently is a critical problem that hinders the development of FMEC. To address this problem, we sought to introduce an approach to selecting an appropriate security service as per the mobile user requirements in FMEC. The problem of appropriate security service selection with hesitant fuzzy information is a multi-criteria decision making problem. In this paper, we introduce a soft hesitant fuzzy rough set (SHFRS) to solve multi-criteria decision making problems. SHFRS is introduced as an innovative extension of the hesitant fuzzy rough set theory by fusing it with the hesitant fuzzy soft set. We describe the inverse hesitant fuzzy soft set that defines the inverse hesitant fuzzy relation to determine the SHFRS upper and lower approximation operators of any hesitant fuzzy subset in the given set of parameters. We also present different special cases of SHFRS upper and lower approximation operators and discuss some fundamental theorems based on approximation operators. In addition, we propose a novel solution to multi-criteria decision making problems based on SHFRS. Finally, we assess the proposed solution by applying it to a real-time multi-criteria decision making problem of appropriate security service selection for FMEC in the existence of multi-observer hesitant fuzzy information.

A Hesitant Fuzzy Based Security Approach for Fog and Mobile-Edge Computing