Adaptive fuzzy rule-based classification systems

This paper proposes an adaptive method to construct a fuzzy rule-based classification system with high performance for pattern classification problems. The proposed method consists of two procedures: an error correction-based learning procedure, and an additional learning procedure. The error correction-based learning procedure adjusts the grade of certainty of each fuzzy rule by its classification performance. That is, when a pattern is misclassified by a particular fuzzy rule, the grade of certainty of that rule is decreased. On the contrary, when a pattern is correctly classified, the grade of certainty is increased. Because the error correction-based learning procedure is not meaningful after all the given patterns are correctly classified, we cannot adjust a classification boundary in such a case. To acquire a more intuitively acceptable boundary, we propose an additional learning procedure. We also propose a method for selecting significant fuzzy rules by pruning unnecessary fuzzy rules, which consists of the error correction-based learning procedure and the concept of forgetting. We can construct a compact fuzzy rule-based classification system with high performance     

Support vector learning for fuzzy rule-based classification systems

To design a fuzzy rule-based classification system (fuzzy classifier) with good generalization ability in a high dimensional feature space has been an active research topic for a long time. As a powerful machine learning approach for pattern recognition problems, the support vector machine (SVM) is known to have good generalization ability. More importantly, an SVM can work very well on a high- (or even infinite) dimensional feature space. This paper investigates the connection between fuzzy classifiers and kernel machines, establishes a link between fuzzy rules and kernels, and proposes a learning algorithm for fuzzy classifiers. We first show that a fuzzy classifier implicitly defines a translation invariant kernel under the assumption that all membership functions associated with the same input variable are generated from location transformation of a reference function. Fuzzy inference on the IF-part of a fuzzy rule can be viewed as evaluating the kernel function. The kernel function is then proven to be a Mercer kernel if the reference functions meet a certain spectral requirement. The corresponding fuzzy classifier is named positive definite fuzzy classifier (PDFC). A PDFC can be built from the given training samples based on a support vector learning approach with the IF-part fuzzy rules given by the support vectors. Since the learning process minimizes an upper bound on the expected risk (expected prediction error) instead of the empirical risk (training error), the resulting PDFC usually has good generalization. Moreover, because of the sparsity properties of the SVMs, the number of fuzzy rules is irrelevant to the dimension of input space. In this sense, we avoid the "curse of dimensionality." Finally, PDFCs with different reference functions are constructed using the support vector learning approach. The performance of the PDFCs is illustrated by extensive experimental results. Comparisons with other methods are also provided.     

An ensemble method for fuzzy rule-based classification systems

Fuzzy rule-based classification systems are very useful tools in the field of machine learning as they are able to build linguistic comprehensible models. However, these systems suffer from exponential rule explosion when the number of variables increases, degrading, therefore, the accuracy of these systems as well as their interpretability. In this article, we propose to improve the comprehensibility through a supervised learning method by automatic generation of fuzzy classification rules, designated SIFCO–PAF. Our method reduces the complexity by decreasing the number of rules and of antecedent conditions, making it thus adapted to the representation and the prediction of rather high-dimensional pattern classification problems. We perform, firstly, an ensemble methodology by combining a set of simple classification models. Subsequently, each model uses a subset of the initial attributes: In this case, we propose to regroup the attributes using linear correlation search among the training set elements. Secondly, we implement an optimal fuzzy partition thanks to supervised discretization followed by an automatic membership functions construction. The SIFCO–PAF method, analyzed experimentally on various data sets, guarantees an important reduction in the number of rules and of antecedents without deteriorating the classification rates, on the contrary accuracy is even improved.     

Supervised methods for regrouping attributes in fuzzy rule-based classification systems

This paper focuses on ensemble methods for Fuzzy Rule-Based Classification Systems (FRBCS) where the decisions of different classifiers are combined in order to form the final classification model. The proposed methods reduce the FRBCS complexity and the generated rules number. We are interested in particular in ensemble methods which cluster the attributes into subgroups of attributes and treat each subgroup separately. Our work is an extension of a previous ensemble method called SIFRA. This method uses frequent itemsets mining concept in order to deduce the groups of related attributes by analyzing their simultaneous appearances in the databases. The drawback of this method is that it forms the groups of attributes by searching for dependencies between the attributes independently from the class information. Besides, since we deal with supervised learning problems, it would be very interesting to consider the class attribute when forming the attributes subgroups. In this paper, we proposed two new supervised attributes regrouping methods which take into account not only the dependencies between the attributes but also the information about the class labels. The results obtained with various benchmark datasets show a good accuracy of the built classification model.     

Effect of rule weights in fuzzy rule-based classification systems

This paper examines the effect of rule weights in fuzzy rule-based classification systems. Each fuzzy IF-THEN rule in our classification system has antecedent linguistic values and a single consequent class. We use a fuzzy reasoning method based on a single winner rule in the classification phase. The winner rule for a new pattern is the fuzzy IF-THEN rule that has the maximum compatibility grade with the new pattern. When we use fuzzy IF-THEN rules with certainty grades, the winner is determined as the rule with the maximum product of the compatibility grade and the certainty grade. In this paper, the effect of rule weights is illustrated by drawing classification boundaries using fuzzy IF-THEN rules with/without certainty grades. It is also shown that certainty grades play an important role when a fuzzy rule-based classification system is a mixture of general rules and specific rules. Through computer simulations, we show that comprehensible fuzzy rule-based systems with high classification performance can be designed without modifying the membership functions of antecedent linguistic values when we use fuzzy IF-THEN rules with certainty grades     

hGA: Hybrid genetic algorithm in fuzzy rule-based classification systems for high-dimensional problems

The aim of this work is to propose a hybrid heuristic approach (called hGA) based on genetic algorithm (GA) and integer-programming formulation (IPF) to solve high dimensional classification problems in linguistic fuzzy rule-based classification systems. In this algorithm, each chromosome represents a rule for specified class, GA is used for producing several rules for each class, and finally IPF is used for selection of rules from a pool of rules, which are obtained by GA. The proposed algorithm is experimentally evaluated by the use of non-parametric statistical tests on seventeen classification benchmark data sets. Results of the comparative study show that hGA is able to discover accurate and concise classification rules.     

Weighted fuzzy interpolative reasoning for sparse fuzzy rule-based systems

In this paper, we present a weighted fuzzy interpolative reasoning method for sparse fuzzy rule-based systems, where the antecedent variables appearing in the fuzzy rules have different weights. We also present a weights-learning algorithm to automatically learn the optimal weights of the antecedent variables of the fuzzy rules for the proposed weighted fuzzy interpolative reasoning method. We also apply the proposed weighted fuzzy interpolative reasoning method and the proposed weights-learning algorithm to handle the truck backer-upper control problem. The experimental results show that the proposed fuzzy interpolative reasoning method using the optimally learned weights by the proposed weights-learning algorithm gets better truck backer-upper control results than the ones by the traditional fuzzy inference system and the existing fuzzy interpolative reasoning methods. The proposed method provides us with a useful way for fuzzy rules interpolation in sparse fuzzy rule-based systems.     

Performance evaluation of fuzzy rule-based classification systems obtained by multi-objective genetic algorithms

In this paper, we examine the classification performance of fuzzy if-then rules selected by a GA-based multi-objective rule selection method. This rule selection method can be applied to high-dimensional pattern classification problems with many continuous attributes by restricting the number of antecedent conditions of each candidate fuzzy if-then rule. As candidate rules, we only use fuzzy if-then rules with a small number of antecedent conditions. Thus it is easy for human users to understand each rule selected by our method. Our rule selection method has two objectives: to minimize the number of selected fuzzy if-then rules and to maximize the number of correctly classified patterns. In our multi-objective fuzzy rule selection problem, there exist several solutions (i.e., several rule sets) called “non-dominated solutions” because two conflicting objectives are considered. In this paper, we examine the performance of our GA-based rule selection method by computer simulations on a real-world pattern classification problem with many continuous attributes. First we examine the classification performance of our method for training patterns by computer simulations. Next we examine the generalization ability for test patterns. We show that a fuzzy rule-based classification system with an appropriate number of rules has high generalization ability.     

Missing data imputation in multivariate data by evolutionary algorithms

This paper presents a proposal based on an evolutionary algorithm to impute missing observations in multivariate data. A genetic algorithm based on the minimization of an error function derived from their covariance matrix and vector of means is presented.All methodological aspects of the genetic structure are presented. An extended explanation of the design of the fitness function is provided. An application example is solved by the proposed method.     

Matrix formulation of fuzzy rule-based systems

In this paper, a matrix formulation of fuzzy rule based systems is introduced. A gradient descent training algorithm for the determination of the unknown parameters can also be expressed in a matrix form for various adaptive fuzzy networks. When converting a rule-based system to the proposed matrix formulation, only three sets of linear/nonlinear equations are required instead of set of rules and an inference mechanism. There are a number of advantages which the matrix formulation has compared with the linguistic approach. Firstly, it obviates the differences among the various architectures; and secondly, it is much easier to organize data in the implementation or simulation of the fuzzy system. The formulation will be illustrated by a number of examples.     

Improving the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets and genetic amplitude tuning

Among the computational intelligence techniques employed to solve classification problems, Fuzzy Rule-Based Classification Systems (FRBCSs) are a popular tool because of their interpretable models based on linguistic variables, which are easier to understand for the experts or end-users.The aim of this paper is to enhance the performance of FRBCSs by extending the Knowledge Base with the application of the concept of Interval-Valued Fuzzy Sets (IVFSs). We consider a post-processing genetic tuning step that adjusts the amplitude of the upper bound of the IVFS to contextualize the fuzzy partitions and to obtain a most accurate solution to the problem.We analyze the goodness of this approach using two basic and well-known fuzzy rule learning algorithms, the Chi et al.’s method and the fuzzy hybrid genetics-based machine learning algorithm. We show the improvement achieved by this model through an extensive empirical study with a large collection of data-sets.     

GP-COACH: Genetic Programming-based learning of COmpact and ACcurate fuzzy rule-based classification systems for High-dimensional problems

In this paper we propose GP-COACH, a Genetic Programming-based method for the learning of COmpact and ACcurate fuzzy rule-based classification systems for High-dimensional problems. GP-COACH learns disjunctive normal form rules (generated by means of a context-free grammar) coded as one rule per tree. The population constitutes the rule base, so it is a genetic cooperative-competitive learning approach. GP-COACH uses a token competition mechanism to maintain the diversity of the population and this obliges the rules to compete and cooperate among themselves and allows the obtaining of a compact set of fuzzy rules. The results obtained have been validated by the use of non-parametric statistical tests, showing a good performance in terms of accuracy and interpretability.     

Evolutionary rule-based systems for imbalanced data sets

This paper investigates the capabilities of evolutionary on-line rule-based systems, also called learning classifier systems (LCSs), for extracting knowledge from imbalanced data. While some learners may suffer from class imbalances and instances sparsely distributed around the feature space, we show that LCSs are flexible methods that can be adapted to detect such cases and find suitable models. Results on artificial data sets specifically designed for testing the capabilities of LCSs in imbalanced data show that LCSs are able to extract knowledge from highly imbalanced domains. When LCSs are used with real-world problems, they demonstrate to be one of the most robust methods compared with instance-based learners, decision trees, and support vector machines. Moreover, all the learners benefit from re-sampling techniques. Although there is not a re-sampling technique that performs best in all data sets and for all learners, those based in over-sampling seem to perform better on average. The paper adapts and analyzes LCSs for challenging imbalanced data sets and establishes the bases for further studying the combination of re-sampling technique and learner best suited to a specific kind of problem.     

缺失值填充:基于信息增益的方法

在数据挖掘以及机器学习等领域,都需要涉及一个数据预处理过程,以消除数据中所包含的错误、噪声、不一致数据或缺失值。其中,缺失值的填充是一个非常具有挑战性的任务,因为填充效果的好坏会极大的影响学习算法及挖掘算法的后续处理过程。目前已有的一些填充算法,如基于粗糙集的和基于最近邻法的算法等,在一定程度上能够处理缺失值问题。与以上方法不同,提出了一种扩展的基于信息增益的缺失值填充算法,它充分利用数据集中各属性之间隐含的关系对缺失的数据进行填充。大量的实验表明,提出的扩展的基于信息增益的缺失值填充算法是有效的。     

Missing data imputation by utilizing information within incomplete instances

This paper proposes to utilize information within incomplete instances (instances with missing values) when estimating missing values. Accordingly, a simple and efficient nonparametric iterative imputation algorithm, called the NIIA method, is designed for iteratively imputing missing target values. The NIIA method imputes each missing value several times until the algorithm converges. In the first iteration, all the complete instances are used to estimate missing values. The information within incomplete instances is utilized since the second imputation iteration. We conduct some experiments for evaluating the efficiency, and demonstrate: (1) the utilization of information within incomplete instances is of benefit to easily capture the distribution of a dataset; and (2) the NIIA method outperforms the existing methods in accuracy, and this advantage is clearly highlighted when datasets have a high missing ratio.     

Structure identification in complete rule-based fuzzy systems

The identification of a model is one of the key issues in the field of fuzzy system modeling and function approximation theory. There are numerous approaches to the issue of parameter optimization within a fixed fuzzy system structure but no reliable method to obtain the optimal topology of the fuzzy system from a set of input-output data. This paper presents a reliable method to obtain the structure of a complete rule-based fuzzy system for a specific approximation accuracy of the training data, i.e., it can decide which input variables must be taken into account in the fuzzy system and how many membership functions (MFs) are needed in every selected input variable in order to reach the approximation target with the minimum number of parameters     

A neuro-fuzzy scheme for simultaneous feature selection and fuzzy rule-based classification

Most methods of classification either ignore feature analysis or do it in a separate phase, offline prior to the main classification task. This paper proposes a neuro-fuzzy scheme for designing a classifier along with feature selection. It is a four-layered feed-forward network for realizing a fuzzy rule-based classifier. The network is trained by error backpropagation in three phases. In the first phase, the network learns the important features and the classification rules. In the subsequent phases, the network is pruned to an "optimal" architecture that represents an "optimal" set of rules. Pruning is found to drastically reduce the size of the network without degrading the performance. The pruned network is further tuned to improve performance. The rules learned by the network can be easily read from the network. The system is tested on both synthetic and real data sets and found to perform quite well.     

A fuzzy rule-based interactive fusion system for seismic data analysis

The study presented in this paper concerns an interactive fusion system that uses the fuzzy set theory to detect regions in three-dimensional seismic images. To achieve detection of regions in 3D seismic images, attributes extracted from images are fused using geophysicist interpreter knowledge by means of a fuzzy rule-based classifier. The original contribution of this work lies in the means proposed to the end-user for tuning the fuzzy membership functions in a two-dimensional universe for particular 2D reference image sections. The proposed graphic user interface allows to obtain a better region detection compared with the detection obtained without fusion. Moreover, a confidence index, based on information theory concepts, is introduced. This index is based on a coefficient of attribute influence and provides some elucidation on how the fusion results have been obtained.