Countering cyber threats, especially attack detection, is a challenging area of research in the field of information assurance. Intruders use polymorphic mechanisms to masquerade the attack payload and evade the detection techniques. Many supervised and unsupervised learning approaches from the field of machine learning and pattern recognition have been used to increase the efficacy of intrusion detection systems (IDSs). Supervised learning approaches use only labeled samples to train a classifier, but obtaining sufficient labeled samples is cumbersome, and requires the efforts of domain experts. However, unlabeled samples can easily be obtained in many real world problems. Compared to supervised learning approaches, semi-supervised learning (SSL) addresses this issue by considering large amount of unlabeled samples together with the labeled samples to build a better classifier. This paper proposes a novel fuzziness based semi-supervised learning approach by utilizing unlabeled samples assisted with supervised learning algorithm to improve the classifier’s performance for the IDSs. A single hidden layer feed-forward neural network (SLFN) is trained to output a fuzzy membership vector, and the sample categorization (low, mid, and high fuzziness categories) on unlabeled samples is performed using the fuzzy quantity. The classifier is retrained after incorporating each category separately into the original training set. The experimental results using this technique of intrusion detection on the NSL-KDD dataset show that unlabeled samples belonging to low and high fuzziness groups make major contributions to improve the classifier’s performance compared to existing classifiers e.g., naive bayes, support vector machine, random forests, etc.
Rough set theory and fuzzy set theory are two useful mathematical tools for dealing with uncertainty and granularity in information systems. Motivated by the studies of roughness and fuzziness in algebraic systems and partially ordered sets such as semigroups, rings and lattices, in this paper we introduce first the notions of fuzzy (prime, semi-prime, primary) ideals of quantales and investigate their properties. Several characterizations of such ideals are presented. Then, we introduce the concepts of weak fuzzy prime ideals and strong fuzzy prime ideals of quantales, and establish relationships between these ideals and fuzzy prime ideals of quantales. By applying rough set theory to fuzzy ideals of quantales, we furthermore define rough fuzzy (prime, semi-prime, primary) ideals of quantales, generalizing Yang and Xu’s work on quantales to the fuzzy environment. Finally, relationships between the upper (resp. lower) rough fuzzy ideals of quantales and the upper (resp. lower) approximations of their homomorphic images are also discussed.
In this paper, we concentrate on the usage of uncertainty associated with the level of fuzziness in determination of the number of clusters in FCM for any data set. We propose a MiniMax -stable cluster validity index based on the uncertainty associated with the level of fuzziness within the framework of interval valued Type 2 fuzziness. If the data have a clustered structure, the optimum number of clusters may be assumed to have minimum uncertainty under upper and lower levels of fuzziness. Upper and lower values of the level of fuzziness for Fuzzy -Mean (FCM) clustering methodology have been found as = 2.6 and 1.4, respectively, in our previous studies. Our investigation shows that the stability of cluster centers with respect to the level of fuzziness is sufficient for the determination of the number of clusters.
The wide usage of relational databases motivated researchers to develop more user friendly interfaces which would allow a larger population of users to access databases. Such interfaces range from visual to natural language based. This paper contributes a question driven query model which falls under the natural language based category. The proposed model supports fuzziness where every user is given the freedom to define his/her own understanding of fuzzy terms. The developed system captures the fuzzy understanding of each user to utilize it while deciding on the result to be communicated back as answer to a raised question. Data mining techniques are employed to guide users in defining their fuzzy understanding. The developed model is intended to help users to retrieve data from a relational database without expecting them to know SQL. The system handles different types of questions, including (1) simple questions, (2) complex questions with inner joins and where conditions, (3) questions that involve usage of aggregate functions (e.g., min, max, etc.), and (4) questions with fuzzy terms. The reported test results demonstrate the effectiveness and applicability of the developed system in handling various types of questions raised by a heterogeneous set of users ranging from professional to naive.
Semi-supervised learning can be described from different perspectives, which plays a crucial role in the study of machine learning. In this study, a new aspect of semi-supervised learning is explored by investigating the divide-and-conquer strategy based on fuzziness to improve the performance of classifiers. In such an approach, adding a category of samples with low fuzziness in the training set can improve the training accuracy, which is experimentally confirmed and explained in the theory of learning from noisy data. The significance of initial accuracy of a base classifier in improving classifier’s performance is further studied. It is observed that the initial accuracy of a base classifier has a significant impact on the improvement of classifier’s performance. Experimental results exhibit that the improvement of accuracy, which is sensitive to the base classifier, attains its maximum when the initial accuracy is between 70% and 80%.
In this paper, we propose a method to construct a polygonal rough-fuzzy set from a set of polygonal fuzzy sets representing the aggregation of multiple experts’ opinions and propose a new fuzzy interpolative reasoning method for sparse fuzzy rule-based systems based on the ratio of fuzziness of the constructed polygonal rough-fuzzy sets, where the values of the antecedent variables and the consequence variable appearing in the fuzzy rules are represented by the constructed polygonal rough-fuzzy sets. The proposed fuzzy interpolative reasoning method can overcome the drawbacks of the existing method due to the fact that it can deal with fuzzy interpolative reasoning using polygonal rough-fuzzy sets and it gets more reasonable fuzzy interpolative reasoning results than the existing method.
The level of fuzziness is a parameter in fuzzy system modeling which is a source of uncertainty. In order to explore the effect of this uncertainty, one needs to investigate and identify effective upper and lower boundaries of the level of fuzziness. For this purpose, Fuzzy -means (FCM) clustering methodology is investigated to determine the effective upper and lower boundaries of the level of fuzziness in order to capture the uncertainty generated by this parameter. In this regard, we propose to expand the membership function around important information points of FCM. These important information points are, cluster centers and the mass center. At these points, it is known that, the level of fuzziness has no effect on the membership values. In this way, we identify the counter-intuitive behavior of membership function near these particular information points. It will be shown that the upper and lower values of the level of fuzziness can be identified. Hence the uncertainty generated by this parameter can be encapsulated.
This paper proposes a technique to deal with fuzziness in subjective evaluation data, and applies it to principal component analysis and correspondence analysis. In the existing method, or techniques developed directly from it, fuzzy sets are defined from some standpoint on a data space, and the fuzzy parameters of the statistical model are identified with linear programming or the method of least squares. In this paper, we try to map the variation in evaluation data into the parameter space while preserving information as much as possible, and thereby define fuzzy sets in the parameter space. Clearly, it is possible to use the obtained fuzzy model to derive things like the principal component scores from the extension principle. However, with a fuzzy model which uses the extension principle, the possibility distribution spreads out as the explanatory variable values increase. This does not necessarily make sense for subjective evaluations, such as a 5-level evaluation, for instance. Instead of doing so, we propose a method for explicitly expressing the vagueness of evaluation, using certain quantities related to the eigenvalues of a matrix which specifies the fuzzy parameter spread. As a numerical example, we present an analysis of subjective evaluation data on local environments.
In this paper, we concentrate on the usage of uncertainty associated with the level of fuzziness in determination of the number of clusters in FCM for any data set. We propose a MiniMax I[micro]-stable cluster validity index based on the uncertainty associated with the level of fuzziness within the framework of interval valued Type 2 fuzziness. If the data have a clustered structure, the optimum number of clusters may be assumed to have minimum uncertainty under upper and lower levels of fuzziness. Upper and lower values of the level of fuzziness for Fuzzy C-Mean (FCM) clustering methodology have been found as m =2.6 and 1.4, respectively, in our previous studies. Our investigation shows that the stability of cluster centers with respect to the level of fuzziness is sufficient for the determination of the number of clusters.