Combining boosting and evolutionary algorithms for learning of fuzzy classification rules

The process of monitoring the events occurring in a computer system or network and analyzing them for sign of intrusions is known as intrusion detection system (IDS). The objective of this paper is to extract fuzzy classification rules for intrusion detection in computer networks. The proposed method is based on the iterative rule learning approach (IRL) to fuzzy rule base system design. The fuzzy rule base is generated in an incremental fashion, in that the evolutionary algorithm optimizes one fuzzy classifier rule at a time. The performance of final fuzzy classification system has been investigated using intrusion detection problem as a high-dimensional classification problem. Results show that the presented algorithm produces fuzzy rules, which can be used to construct a reliable intrusion detection system.

An interpretability improvement for fuzzy rule bases obtained by the iterative rule learning approach

The central point in designing a fuzzy system for modeling and control is the generation of a set of efficient and effective fuzzy rules. Generally, fuzzy rules can be generated either from heuristics or from experimental data. Heuristic fuzzy rule generation, as discussed in Chapter 1, consists of the following main steps: Determination of the structure of the fuzzy systems. This includes mainly the selection of the inputs and outputs. Usually, a multi-input multi-output fuzzy systems can be decomposed into a number of multi-input single-output fuzzy systems. Definition of linguistic terms and their fuzzy membership function for each fuzzy variables. If a Mamdani fuzzy system is designed, each input and output can be seen as a linguistic variable. Therefore, it is necessary to define the linguistic terms (e.g., Small, Medium, Large etc.) and their fuzzy membership function. Details about the definition of a linguistic variable is presented in Section 1.2.1. Determination of fuzzy inference method. For example, for fuzzy mapping rules, the fuzzy Cartesian product can be used to define the fuzzy relation. Refer to Section 1.2.2. Defuzzification. If the Mamdani type fuzzy rules are used, the fuzzy output derived from the fuzzy rule base should be defuzzified. Refer also to Section 1.2.2 for different defuzzification methods. If the Takagi-Sugeno fuzzy rules are used, the defuzzification is included in the fuzzy inference and a crisp output is obtained directly.

The use of fuzzy rule-based systems in regression problems is widely extended due to the precision of the obtained models. Moreover, the use of Mamdani models is usually referred to as a good choice in many real problems, since it provides an interpretable and precise functional relationship between the output and input variables. In this paper we present a new leaning Mamdani fuzzy system FRLC-Rgress (Fuzzy Rule Learning through Clustering for Regression Problems). This provides an accurate fuzzy system and simple Mamdani fuzzy rule bases for regression problems. FRLC-Rgress based on linguistic modifiers and fuzzy clustering achieves a low complexity of the learned models while keeping a high accuracy, by following two stages: multi- granularity, fuzzy discretization of the variables, and perceptual learning of the fuzzy rules. FRLC-Rgress is experimented using six real-world datasets. It outperforms two of the most and simple fuzzy systems (genetic fuzzy systems) in state of the art.

Inferring descriptive and approximate fuzzy rules for credit scoring using evolutionary algorithms

Fuzzy rules cooperate in a fuzzy logic controller (FLC) to produce the best action for a given situation. If we have a population of fuzzy rules controlling a device, and we would like to evolve the population to obtain optimal performance by reinforcement learning, rules should compete each other, since we would like to judge their proposals. Therefore, in this approach, cooperation and competition are two opposite, desired activities done by the population members. This may be a problem, if we consider that the evaluation function may be biased, as it may happen, for instance, when we are designing a controlled device such as an autonomous agent. The problem becomes even harder if we would like to learn general rules, i.e., rules containing don't care symbols in their antecedents, thus competing with many groups of other rules, in many different situations. We discuss these issues, and present a solution, implemented in ELF (evolutionary learning of fuzzy rules). We successfully applied ELF to develop autonomous agents, and other fuzzy controlled devices. >

This paper presents a fuzzy learning rule which is the fuzzified version of LVQ(Learning Vector Quantization). This fuzzy learning rule 3 uses fuzzy learning rates. instead of the traditional learning rates. LVQ uses the same learning rate regardless of correctness of classification. But, the new fuzzy learning rule uses the different learning rates depending on whether classification is correct or not. The new fuzzy learning rule is integrated into the improved IAFC(Integrated Adaptive Fuzzy Clustering) neural network. The improved IAFC neural network is both stable and plastic. The iris data set is used to compare the performance of the supervised IAFC neural network 3 with the performance of backprogation neural network. The results show that the supervised IAFC neural network 3 is better than backpropagation neural network.

This paper introduces the Fast Iterative Rule-based Linguistic Classifier (FaIRLiC), a Genetic Fuzzy Rule-Based Classification System (GFRBCS) which targets at reducing the structural complexity of the resulting rule base, as well as its learning algorithm's computational requirements, especially when dealing with high-dimensional feature spaces. The proposed methodology follows the principles of the iterative rule learning (IRL) approach, whereby a rule extraction algorithm (REA) is invoked in an iterative fashion, producing one fuzzy rule at a time. The REA is performed in two successive steps: the first one selects the relevant features of the currently extracted rule, whereas the second one decides the antecedent part of the fuzzy rule, using the previously selected subset of features. The performance of the classifier is finally optimized through a genetic tuning post-processing stage. Comparative results in a hyperspectral remote sensing classification as well as in 12 real-world classification datasets indicate the effectiveness of the proposed methodology in generating high-performing and compact fuzzy rule-based classifiers, even for very high-dimensional feature spaces.

One direction of measured data-set based modeling applies fuzzy logic identification tools and results in a fuzzy rule-base model. A typical problem of fuzzy identification methods is that the complexity of the resulting fuzzy rule-base, namely the number of rules in the rule-base, explodes with the modeling accuracy. As a result, the topic of fuzzy rule-base complexity reduction techniques emerged in the last decade. A common disadvantage of fuzzy rule-base complexity reduction methods is that the resulting complexity minimized fuzzy-rule bases cannot be simply adapted to new information. If we have new information that cannot be described by the fuzzy rules of the complexity minimized fuzzy rule-base, then we have two choices. The first choice is to add new fuzzy rules to the fuzzy rule-base until the new information can be described. The second choice is to modify the new information until it can be described by the fuzzy rule-base without using additional fuzzy rules. This second case has the prominent role if the number of fuzzy rules in the fuzzy rule-base is limited. This paper proposes a method for the second choice. The proposed method minimizes the necessary modification of the new information. This paper focuses attention on a recent complexity reduction method, termed Higher Order Singular Value Decomposition (HOSVD)-based complexity reduction, and Takagi-Sugeno (TS) inference operator-based fuzzy rule-bases. An example is used to provide the validation of the proposed method. In order to demonstrate the effectiveness of the proposed method, a control system of a differential-steered automatic guided vehicle is modeled in the paper.

Conventionally modelling and simulation of complex nonlinear systems has been to construct a mathematical model and examine the system’s evolution or its control. This kind of approach can fail for many of the very large non-linear and complex systems being currently studied. With the invention of new advanced high-speed computers and the application of artificial intelligence paradigms new techniques have become available. Particularly neural networks and fuzzy logic for nonlinear modelling and genetic algorithms [Goldberg, D. (1989)] and evolutionary algorithms for optimisation methods have created new opportunities to solve complex systems [Bai, Y., Zhuang H. and Wang, D. (2006)]. This paper considers issues in design of multi-layer and hierarchical fuzzy logic systems. It proposes a decomposition technique for complex systems into hierarchical and multi-layered fuzzy logic sub-systems. The learning of fuzzy rules and internal parameters in a supervised manner is performed using genetic algorithms. The decomposition of complex nonlinear systems into hierarchical and multi-layered fuzzy logic sub-systems reduces greatly the number of fuzzy rules to be defined and improves the learning speed for such systems. In this paper a method for combining subsystems to create a hierarchical and multilayer fuzzy logic system is also described. Application areas considered are - the prediction of interest rate, unemployment rate predication and electricity usage prediction. Genetic Algorithms can be used as a tool for design and generation of fuzzy rules for a fuzzy logic system. This automatic design and generation of fuzzy rules, via genetic algorithms, can be categorised into two learning techniques namely, supervised and unsupervised. In supervised learning there are two distinct phases to the operation. In the first phase each individual is assessed based on the input signal that is propagated through the system producing output respond. The actual respond produced is then compared with a desired response, generating error signals that are then used as the fitness for the individual in the population of genetic algorithms. Supervised learning has successfully applied to solve some difficult problems. In this paper design and development of a genetic algorithm based supervised learning for fuzzy models with application to several problems is considered. A hybrid integrated architecture incorporating fuzzy logic and genetic algorithm can generate fuzzy rules that can be used in a fuzzy logic system for modelling, control and prediction

Learning fuzzy rules from iterative execution of games

Granularrules have been extensively used for classification in fuzzy datasets to promote the advancement of artificial intelligence. However, due to the diversity of data types, how to improve the readability of the extracted granular rules while ensuring efficiency is always a challenge. Since granular reduct in granular computing (GrC) can simplify real complex problem and dataset, this article carries out granular rule learning from the perspective of granular reduct by taking formal concept analysis (FCA)-based GrC method as a framework. Specifically, for achieving classification task, we first propose a method to update the granular reduct, and then explore the updating mechanism of fuzzy granular rule in a reduced dataset. Second, a novel fuzzy rule-based classification model named FRCM is presented for fuzzy granular rule learning. In order to verify the effectiveness of the proposed model, some numerical experiments for incremental learning and fuzzy rule mining are conducted to demonstrate that FRCM can achieve the state-of-the-art classification performance.

Fuzzy modelling research has traditionally focused on certain types of fuzzy rules. However, the use of alternative rule models could improve the ability of fuzzy systems to represent a specific problem. In this proposal, an extended fuzzy rule model, that can include relations between variables in the antecedent of rules is presented. Furthermore, a learning algorithm based on the iterative genetic approach which is able to represent the knowledge using this model is proposed as well. On the other hand, potential relations among initial variables imply an exponential growth in the feasible rule search space. Consequently, two filters for detecting relevant potential relations are added to the learning algorithm. These filters allows to decrease the search space complexity and increase the algorithm efficiency. Finally, we also present an experimental study to demonstrate the benefits of using fuzzy relational rules.

This paper discusses fuzzy reasoning for approximately realizing nonlinear functions by a small number of fuzzy if-then rules with different specificity levels. Our fuzzy rule base is a mixture of general and specific rules, which overlap with each other in the input space. General rules work as default rules in our fuzzy rule base. First, we briefly describe existing approaches to the handling of default rules in the framework of possibility theory. Next, we show that standard interpolation-based fuzzy reasoning leads to counterintuitive results when general rules include specific rules with different consequents. Then, we demonstrate that intuitively acceptable results are obtained from a non-standard inclusion-based fuzzy reasoning method. Our approach is based on the preference for more specific rules, which is a commonly used idea in the field of default reasoning. When a general rule includes a specific rule and they are both compatible with an input vector, the weight of the general rule is discounted in fuzzy reasoning. We also discuss the case where general rules do not perfectly but partially include specific rules. Then we propose a genetics-based machine learning (GBML) algorithm for extracting a small number of fuzzy if-then rules with different specificity levels from numerical data using our inclusion-based fuzzy reasoning method. Finally, we describe how our approach can be applied to the approximate realization of fuzzy number-valued nonlinear functions

Knowledge acquisition is a bottleneck in knowledge-based system implementation. Decision tree induction is a useful machine learning approach for extracting classification knowledge from a set of training examples. Many real-world data contain fuzziness due to observation error, uncertainty, subjective judgement, and so on. To cope with this problem of real-world data, there have been some works on fuzzy classification rule learning. This paper makes a survey for the kinds of fuzzy classification rules. In addition, it presents a fuzzy classification rule learning method based on decision tree induction, and shows some experiment results for the method.