New Fermatean Fuzzy Distance Metric and Its Utilization in the Assessment of Security Crises Using the MCDM Technique

The problem of insecurity is a global phenomenon that has several forms like terrorism, banditry, kidnappings, etc. Insecurity has taken hold in the Sub-Saharan Region of West Africa, especially in Nigeria, for over two decades. Nigeria’s security crisis is more pronounced in the Northern Region, with a new wave in the North-Central Region of Nigeria. It is herculean to assess insecurity in the North-Central Region of Nigeria because of the region’s fuzzy or imprecise nature of insecurity. This constitutes the rationale for deploying the Fermatean fuzzy technique to assess insecurity due to the capacity of the Fermatean fuzzy scheme to handle imprecision. To this end, a new Fermatean fuzzy distance metric is presented to evaluate insecurity in the North-Central Region of Nigeria using a multi-criteria decision-making technique. To express the logic for creating the new Fermatean fuzzy distance metric, some existing Fermatean fuzzy distance metrics are discussed, along with their drawbacks. The mathematical properties of the new technique are discussed, and the new method is applied computationally to assess insecurity in the North-Central Region of Nigeria. The data for the security assessment are collected via Fermatean fuzzy linguistic variables using the opinions of security experts and analyzed using the technique for order of preference by similarity to ideal solution, which is a commonly used multi-criteria decision-making method. Finally, the numerical validity of the new technique is expressed with comparative results, and the finding shows the benefit of the new distance approach over the existing methodologies. The outcome of the work will provide reliable traveling advisories for safe voyages within the region.