A Threefold Approach for Enhancing Fuzzy Interpolative Reasoning: Case Study on Phishing Attack Detection Using Sparse Rule Bases

Fuzzy systems are powerful modeling systems for uncertainty applications. In contrast to traditional crisp systems, fuzzy systems offer the opportunity to extend the binary decision to continuous space, which could offer benefits for various application areas such as intrusion detection systems (IDSs), because of their ability to measure the degree of attacks instead of making a binary decision. Furthermore, fuzzy systems offer a suitable environment that is able to deal with uncertainty. However, fuzzy systems face a critical challenge represented by the sparse fuzzy rules. Typical fuzzy systems demand complete fuzzy rules in order to offer the required results. Additionally, generating complete fuzzy rules can be difficult due to many factors, such as a lack of knowledge base or limited data availability, such as in IDS applications. Fuzzy rule interpolation (FRI) was introduced to overcome this limitation by generating the required interpolation results in cases with sparse fuzzy rules. This work introduces a threefold approach designed to address the cases of missing fuzzy rules, which uses a few fuzzy rules to handle the limitations of missing fuzzy rules. This is achieved by finding the interpolation condition of neighboring fuzzy rules. This procedure was accomplished based on the concept of factors (which determine the degree to which each neighboring fuzzy rule contributes to the interpolated results, in cases of missing fuzzy rules). The evaluation procedure for the threefold approach was conducted using the following two steps: firstly, using the FRI benchmark numerical metrics, the results demonstrated the ability of the threefold approach to generate the required results for the various benchmark scenarios. Secondly, using a real-life dataset (phishing attacks dataset), the results demonstrated the effectiveness of the suggested approach to handle cases of missing fuzzy rules in the area of phishing attacks. Consequently, the suggested threefold approach offers an opportunity to reduce the number of fuzzy rules effectively and generate the required results using only a few fuzzy rules.