A New Fuzzy Interpolative Reasoning Method Based on Center of Gravity

Interpolative reasoning methods do not only help reduce the complexity of fuzzy models hut also make inference in sparse-rule based systems possible. This paper presents an interpolative reasoning method by exploiting the center of gravity (COG) property of the fuzzy sets concerned. The method works by first constructing a new inference rule via manipulating two given adjacent rules, and then by using similarity information to convert the intermediate inference results into the final derived conclusion. Two transformation operations are introduced to support such reasoning, which allow the COG of a fuzzy set to remain unaltered before and after the transformation, Results of experimental comparisons are provided to reflect the success of this work

Fuzzy interpolative reasoning via scale and move transformation

Interpolative reasoning does not only help reduce the complexity of fuzzy models but also makes inference in sparse rule-based systems possible. This paper presents an interpolative reasoning method by means of scale and move transformations. It can be used to interpolate fuzzy rules involving complex polygon, Gaussian or other bell-shaped fuzzy membership functions. The method works by first constructing a new inference rule via manipulating two given adjacent rules, and then by using scale and move transformations to convert the intermediate inference results into the final derived conclusions. This method has three advantages thanks to the proposed transformations: 1) it can handle interpolation of multiple antecedent variables with simple computation; 2) it guarantees the uniqueness as well as normality and convexity of the resulting interpolated fuzzy sets; and 3) it suggests a variety of definitions for representative values, providing a degree of freedom to meet different requirements. Comparative experimental studies are provided to demonstrate the potential of this method

Fuzzy Rule Based Interpolative Reasoning Supported by Attribute Ranking

Using fuzzy rule interpolation (FRI) interpolative reasoning can be effectively performed with a sparse rule base where a given system observation does not match any fuzzy rules. Whilst offering a potentially powerful inference mechanism, in the current literature, typical representation of fuzzy rules in FRI assumes that all attributes in the rules are of equal significance in deriving the consequents. This is a strong assumption in practical applications, thereby often leading to less accurate interpolated results. To address this challenging problem, this work employs feature selection (FS) techniques to adjudge the relative significance of individual attributes and therefore, to differentiate the contributions of the rule antecedents and their impact upon FRI. This is feasible because FS provides a readily adaptable mechanism for evaluating and ranking attributes, being capable of selecting more informative features. Without requiring any acquisition of real observations, based on the originally given sparse rule base, the individual scores are computed using a set of training samples that are artificially created from the rule base through an innovative reverse engineering procedure. The attribute scores are integrated within the popular scale and move transformation-based FRI algorithm (while other FRI approaches may be similarly extended following the same idea), forming a novel method for attribute ranking-supported fuzzy interpolative reasoning. The efficacy and robustness of the proposed approach is verified through systematic experimental examinations in comparison with the original FRI technique, over a range of benchmark classification problems while utilising different FS methods. A specific and important outcome is that supported by attribute ranking, only two (i.e., the least number of) nearest adjacent rules are required to perform accurate interpolative reasoning, avoiding the need of searching for and computing with multiple rules beyond the immediate neighbourhood of a given observationpublishersversionPeer reviewe

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

Transformation-Based Fuzzy Rule Interpolation With Mahalanobis Distance Measures Supported by Choquet Integral

Fuzzy rule interpolation (FRI) strongly supports approximate inference when a new observation matches no rules, through selecting and subsequently interpolating appropriate rules close to the observation from the given (sparse) rule base. Traditional ways of implementing the critical rule selection process are typically based on the exploitation of Euclidean distances between the observation and rules. It is conceptually straightforward for implementation but applying this distance metric may systematically lead to inferior results because it fails to reflect the variations of the relevance or significance levels amongst different domain features. To address this important issue, a novel transformation-based FRI approach is presented, on the basis of utilising the Mahalanobis distance metric. The new FRI method works by transforming a given sparse rule base into a coordinates system where the distance between instances of the same category becomes closer while that between different categories becomes further apart. In so doing, when an observation is present that matches no rules, the most relevant neighbouring rules to implement the required interpolation are more likely to be selected. Following this, the scale and move factors within the classical transformation-based FRI procedure are also modified by Choquet integral. Systematic experimental investigation over a range of classification problems demonstrates that the proposed approach remarkably outperforms the existing state-of-the-art FRI methods in both accuracy and efficiency