Towards sparse rule base generation for fuzzy rule interpolation

Fuzzy inference systems have been successfully applied to many real-world applications. Traditional fuzzy inference systems are only applicable to problems with dense rule bases by which the entire input domain is fully covered, whilst fuzzy rule interpolation (FRI) is also able to work with sparse rule bases that may not cover certain observations. Thanks to their abilities to work with fewer rules, FRI approaches have also been utilised to reduce system complexity by removing those rules which can be approximated by their neighbouring ones for complex fuzzy models. A number of important fuzzy rule base generation approaches have been proposed in the literature, but the majority of these only target dense rule bases for traditional fuzzy inference systems. This paper proposes a novel sparse fuzzy rule base generation method to support FRI. The approach first identifies important rules that cannot be accurately approximated by their neighbouring ones to initialise the rule base. Then the raw rule base is optimised by fine tuning the membership functions of the fuzzy sets. Experimentation is conducted to demonstrate the working principles of the proposed system, with results comparable to those of traditional methods

Dynamic fuzzy rule interpolation and its application to intrusion detection

Fuzzy rule interpolation (FRI) offers an effective approach for making inference possible in sparse rule-based systems (and also for reducing the complexity of fuzzy models). However, requirements of fuzzy systems may change over time and hence, the use of a static rule base may affect the accuracy of FRI applications. Fortunately, an FRI system in action will produce interpolated rules in abundance during the interpolative reasoning process. While such interpolated results are discarded in existing FRI systems, they can be utilized to facilitate the development of a dynamic rule base in supporting subsequent inference. This is because the otherwise relinquished interpolated rules may contain possibly valuable information, covering regions that were uncovered by the original sparse rule base. This paper presents a dynamic fuzzy rule interpolation (D-FRI) approach by exploiting such interpolated rules in order to improve the overall system's coverage and efficacy. The resulting D-FRI system is able to select, combine, and generalize informative, frequently used interpolated rules for merging with the existing rule base while performing interpolative reasoning. Systematic experimental investigations demonstrate that D-FRI outperforms conventional FRI techniques, with increased accuracy and robustness. Furthermore, D-FRI is herein applied for network security analysis, in devising a dynamic intrusion detection system (IDS) through integration with the Snort software, one of the most popular open source IDSs. This integration, denoted as D-FRI-Snort hereafter, delivers an extra amount of intelligence to predict the level of potential threats. Experimental results show that with the inclusion of a dynamic rule base, by generalising newly interpolated rules based on the current network traffic conditions, D-FRI-Snort helps reduce both false positives and false negatives in intrusion detection