Rough Fermatean fuzzy decision-based approach for modelling IDS classifiers in the federated learning of IoMT applications

Intrusion detection systems (IDSs) are commonly employed to mitigate network security threats in various fields, including federated learning applications within the Internet of Medical Things (IoMT). However, IDSs face challenges owing to the sheer volume of network traffic, high-dimensional datasets and the necessity for real-time detection. Although machine learning integration assists IDSs in overcoming these challenges, modelling difficulties persist due to varied evaluation criteria and levels of conflict and importance. Multi-criteria decision-making (MCDM) solutions have been utilised in IoMT and IDS, yet they fall short in capturing the subjective judgements of experts and rely on normalisation approaches, which can impact results. This study seeks to address these issues through the integration of robust MCDM methodologies, namely fuzzy-weighted zero-inconsistency (FWZIC) and fuzzy decision by opinion score method (FDOSM). Utilising rough Fermatean fuzzy sets (RFFSs), this integration produces precise solutions with reduced uncertainty. Our methodology involves adopting a decision matrix for IDS classifiers based on integrated evaluation criteria, followed by deriving new formulations and developments for RFFSs-based FDOSM and FWZIC for the modelling and weighting of criteria, respectively. Evaluations using datasets involving 125,973 records and 41 features across 17 evaluation criteria revealed that accuracy–security and training time–performance weights yielded the highest scores, whereas false negative rate–security and CPU time–performance criteria received the lowest weights. The random forest emerged as the optimal IDS classifier. Systematic modelling, sensitivity analysis and comparative studies confirmed the robustness of our results.