An extension of the naive Bayesian classifier

Our objective here is to provide an extension of the naive Bayesian classifier in a manner that gives us more parameters for matching data. We first describe the naive Bayesian classifier, and then discuss the ordered weighted averaging (OWA) aggregation operators. We introduce a new class of OWA operators which are based on a combining the OWA operators with t-norm’s operators. We show that the naive Bayesian classifier can seen as a special case of this. We use this to suggest an extended version of the naive Bayesian classifier which involves a weighted summation of products of the probabilities. An algorithm is suggested to obtain the weights associated with this extended naive Bayesian classifier.     

An initial comparison of a fuzzy neural classifier and a decision tree based classifier

At the present time a large number of AI methods have been developed in the field of pattern classification. In this paper, we will compare the performance of a well-known algorithm in machine learning (C4.5) with a recently proposed algorithm in the fuzzy set community (NEFCLASS). We will compare the algorithms both on the accuracy attained and on the size of the induced rule base. Additionally, we will investigate how the selected algorithms perform after they have been pre-processed by discretization and feature selection.     

One-against-one fuzzy support vector machine classifier: An approach to text categorization

The growth of the internet information delivery has made automatic text categorization essential. This investigation explores the challenges of multi-class text categorization using one-against-one fuzzy support vector machine with Reuter’s news as the example data. The performances of four different membership functions on one-against-one fuzzy support vector machine are measured using the macro-average performance indices. Analytical results indicate that the proposed method achieves a comparable or better performance than the one-against-one support vector machine.     

An efficient fuzzy classifier with feature selection based on fuzzyentropy

This paper presents an efficient fuzzy classifier with the ability of feature selection based on a fuzzy entropy measure. Fuzzy entropy is employed to evaluate the information of pattern distribution in the pattern space. With this information, we can partition the pattern space into nonoverlapping decision regions for pattern classification. Since the decision regions do not overlap, both the complexity and computational load of the classifier are reduced and thus the training time and classification time are extremely short. Although the decision regions are partitioned into nonoverlapping subspaces, we can achieve good classification performance since the decision regions can be correctly determined via our proposed fuzzy entropy measure. In addition, we also investigate the use of fuzzy entropy to select relevant features. The feature selection procedure not only reduces the dimensionality of a problem but also discards noise-corrupted, redundant and unimportant features. Finally, we apply the proposed classifier to the Iris database and Wisconsin breast cancer database to evaluate the classification performance. Both of the results show that the proposed classifier can work well for the pattern classification application.     

Compact fuzzy association rule-based classifier

Classification is one of the most popular data mining techniques applied to many scientific and industrial problems. The efficiency of a classification model is evaluated by two parameters, namely the accuracy and the interpretability of the model. While most of the existing methods claim their accurate superiority over others, their models are usually complex and hardly understandable for the users. In this paper, we propose a novel classification model that is based on easily interpretable fuzzy association rules and fulfils both efficiency criteria. Since the accuracy of a classification model can be largely affected by the partitioning of numerical attributes, this paper discusses several fuzzy and crisp partitioning techniques. The proposed classification method is compared to 15 previously published association rule-based classifiers by testing them on five benchmark data sets. The results show that the fuzzy association rule-based classifier presented in this paper, offers a compact, understandable and accurate classification model.     

Solution of fuzzy matrix games: An application of the extension principle

Conventional game theory is concerned with how rational individuals make decisions when they are faced with known payoffs. This article develops a solution method for the two‐person zero‐sum game where the payoffs are only approximately known and can be represented by fuzzy numbers. Because the payoffs are fuzzy, the value of the game is fuzzy as well. Based on the extension principle, a pair of two‐level mathematical programs is formulated to obtain the upper bound and lower bound of the value of the game at possibility level α. By applying a dual formulation and a variable substitution technique, the pair of two‐level mathematical programs is transformed to a pair of ordinary one‐level linear programs so they can be manipulated. From different values of α, the membership function of the fuzzy value of the game is constructed. It is shown that the two players have the same fuzzy value of the game. An example illustrates the whole idea of a fuzzy matrix game. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 891–903, 2007.     

Genetic tuning of fuzzy inference within fuzzy classifier systems

Abstract: In generating a suitable fuzzy classifier system, significant effort is often placed on the determination and the fine tuning of the fuzzy sets. However, in such systems little thought is given to the way in which membership functions are combined within the fuzzy rules. Often traditional fuzzy inference strategies are used which consequently provide no control over how strongly or weakly the inference is applied within these rules. Furthermore such strategies will allow no interaction between grades of membership. A number of theoretical fuzzy inference operators have been proposed for both regression and classification problems but they have not been investigated in the context of real-world applications. In this paper we propose a novel genetic algorithm framework for optimizing the strength of fuzzy inference operators concurrently with the tuning of membership functions for a given fuzzy classifier system. Each fuzzy system is generated using two well-established decision tree algorithms: C4.5 and CHAID. This will enable both classification and regression problems to be addressed within the framework. Each solution generated by the genetic algorithm will produce a set of fuzzy membership functions and also determine how strongly the inference will be applied within each fuzzy rule. We investigate several theoretical proven fuzzy inference techniques (T-norms) in the context of both classification and regression problems. The methodology proposed is applied to a number of real-world data sets in order to determine the effects of the simultaneous tuning of membership functions and inference parameters on the accuracy and robustness of fuzzy classifiers.     

A design of granular fuzzy classifier

In this paper, we propose a new design methodology of granular fuzzy classifiers based on a concept of information granularity and information granules. The classifier uses the mechanism of information granulation with the aid of which the entire input space is split into a collection of subspaces. When designing the proposed fuzzy classifier, these information granules are constructed in a way they are made reflective of the geometry of patterns belonging to individual classes. Although the elements involved in the generated information granules (clusters) seem to be homogeneous with respect to the distribution of patterns in the input (feature) space, they still could exhibit a significant level of heterogeneity when it comes to the class distribution within the individual clusters. To build an efficient classifier, we improve the class homogeneity of the originally constructed information granules (by adjusting the prototypes of the clusters) and use a weighting scheme as an aggregation mechanism.     

An efficient quantum neuro-fuzzy classifier based on fuzzy entropy and compensatory operation

In this paper, a quantum neuro-fuzzy classifier (QNFC) for classification applications is proposed. The proposed QNFC model is a five-layer structure, which combines the compensatory-based fuzzy reasoning method with the traditional Takagi–Sugeno–Kang (TSK) fuzzy model. The compensatory-based fuzzy reasoning method uses adaptive fuzzy operations of neuro-fuzzy systems that can make the fuzzy logic system more adaptive and effective. Layer 2 of the QNFC model contains quantum membership functions, which are multilevel activation functions. Each quantum membership function is composed of the sum of sigmoid functions shifted by quantum intervals. A self-constructing learning algorithm, which consists of the self-clustering algorithm (SCA), quantum fuzzy entropy and the backpropagation algorithm, is also proposed. The proposed SCA method is a fast, one-pass algorithm that dynamically estimates the number of clusters in an input data space. Quantum fuzzy entropy is employed to evaluate the information on pattern distribution in the pattern space. With this information, we can determine the number of quantum levels. The backpropagation algorithm is used to tune the adjustable parameters. The simulation results have shown that (1) the QNFC model converges quickly; (2) the QNFC model has a higher correct classification rate than other models.     

A fuzzy classifier with ellipsoidal regions

In this paper, we discuss a fuzzy classifier with ellipsoidal regions which has a learning capability. First, we divide the training data for each class into several clusters. Then, for each cluster, we define a fuzzy rule with an ellipsoidal region around a cluster center. Using the training data for each cluster, we calculate the center and the covariance matrix of the ellipsoidal region for the cluster. Then we tune the fuzzy rules, i.e., the slopes of the membership functions, successively until there is no improvement in the recognition rate of the training data. We evaluate our method using the Fisher iris data, numeral data of vehicle license plates, thyroid data, and blood cell data. The recognition rates (except for the thyroid data) of our classifier are comparable to the maximum recognition rates of the multilayered neural network classifier and the training times (except for the iris data) are two to three orders of magnitude shorter     

An /spl epsiv/-margin nonlinear classifier based on fuzzy if-then rules

This paper introduces a new classifier design methods that are based on a modification of the classical Ho-Kashyap procedure. First, it proposes a method to design a linear classifier using the absolute loss rather than the squared loss that results in a better approximation of the misclassification error and robustness of outliers. Additionally, easy control of the generalization ability is obtained by minimization of the Vapnik-Chervonenkis dimension. Next, an extension to a nonlinear classifier by an ensemble averaging technique is presented. Each classifier is represented by a fuzzy if-then rule in the Takagi-Sugeno-Kang form. Two approaches to the estimation of parameters value are used: local, where each of the if-then rule parameters are determined independently and global where all rules are obtained simultaneously. Finally, examples are given to demonstrate the validity of the introduced methods.     

Fuzzy relational classifier trained by fuzzy clustering

A novel approach to nonlinear classification is presented, in the training phase of the classifier, the training data is first clustered in an unsupervised way by fuzzy c-means or a similar algorithm. The class labels are not used in this step. Then, a fuzzy relation between the clusters and the class identifiers is computed. This approach allows the number of prototypes to be independent of the number of actual classes. For the classification of unseen patterns, the membership degrees of the feature vector in the clusters are first computed by using the distance measure of the clustering algorithm. Then, the output fuzzy set is obtained by relational composition. This fuzzy set contains the membership degrees of the pattern in the given classes. A crisp decision is obtained by defuzzification, which gives either a single class or a "reject" decision, when a unique class cannot be selected based on the available information. The principle of the proposed method is demonstrated on an artificial data set and the applicability of the method is shown on the identification of live-stock from recorded sound sequences. The obtained results are compared with two other classifiers.     

一种模糊认知图分类器的研究*

通过使用模糊认知图来模拟分类过程,构造了一种模糊认知图分类器,提出了它的两种模糊认知图分类模型,并在此基础上给出了使用它进行分类的推理机制。实验证明,该方法具有良好的分类性能。     

Face recognition using a fuzzy fisherface classifier

In this study, we are concerned with face recognition using fuzzy fisherface approach and its fuzzy set based augmentation. The well-known fisherface method is relatively insensitive to substantial variations in light direction, face pose, and facial expression. This is accomplished by using both principal component analysis and Fisher's linear discriminant analysis. What makes most of the methods of face recognition (including the fisherface approach) similar is an assumption about the same level of typicality (relevance) of each face to the corresponding class (category). We propose to incorporate a gradual level of assignment to class being regarded as a membership grade with anticipation that such discrimination helps improve classification results. More specifically, when operating on feature vectors resulting from the PCA transformation we complete a Fuzzy K-nearest neighbor class assignment that produces the corresponding degrees of class membership. The comprehensive experiments completed on ORL, Yale, and CNU (Chungbuk National University) face databases show improved classification rates and reduced sensitivity to variations between face images caused by changes in illumination and viewing directions. The performance is compared vis-à-vis other commonly used methods, such as eigenface and fisherface.     

Evolutionary design of a fuzzy classifier from data

Genetic algorithms show powerful capabilities for automatically designing fuzzy systems from data, but many proposed methods must be subjected to some minimal structure assumptions, such as rule base size. In this paper, we also address the design of fuzzy systems from data. A new evolutionary approach is proposed for deriving a compact fuzzy classification system directly from data without any a priori knowledge or assumptions on the distribution of the data. At the beginning of the algorithm, the fuzzy classifier is empty with no rules in the rule base and no membership functions assigned to fuzzy variables. Then, rules and membership functions are automatically created and optimized in an evolutionary process. To accomplish this, parameters of the variable input spread inference training (VISIT) algorithm are used to code fuzzy systems on the training data set. Therefore, we can derive each individual fuzzy system via the VISIT algorithm, and then search the best one via genetic operations. To evaluate the fuzzy classifier, a fuzzy expert system acts as the fitness function. This fuzzy expert system can effectively evaluate the accuracy and compactness at the same time. In the application section, we consider four benchmark classification problems: the iris data, wine data, Wisconsin breast cancer data, and Pima Indian diabetes data. Comparisons of our method with others in the literature show the effectiveness of the proposed method.     

An accuracy-oriented self-splitting fuzzy classifier with support vector learning in high-order expanded consequent space

This paper proposes a self-splitting fuzzy classifier with support vector learning in expanded high-order consequent space (SFC-SVHC) for classification accuracy improvement. The SFC-SVHC expands the rule-mapped consequent space of a first-order Takagi-Sugeno (TS)-type fuzzy system by including high-order terms to enhance the rule discrimination capability. A novel structure and parameter learning approach is proposed to construct the SFC-SVHC. For structure learning, a variance-based self-splitting clustering (VSSC) algorithm is used to determine distributions of the fuzzy sets in the input space. There are no rules in the SFC-SVHC initially. The VSSC algorithm generates a new cluster by splitting an existing cluster into two according to a predefined cluster-variance criterion. The SFC-SVHC uses trigonometric functions to expand the rule-mapped first-order consequent space to a higher-dimensional space. For parameter optimization in the expanded rule-mapped consequent space, a support vector machine is employed to endow the SFC-SVHC with high generalization ability. Experimental results on several classification benchmark problems show that the SFC-SVHC achieves good classification results with a small number of rules. Comparisons with different classifiers demonstrate the superiority of the SFC-SVHC in classification accuracy.     

一类直接构造的模糊多类支持向量分类器

针对直接多类分类方法,提出了一种新的基于直接构造多类SVM分类器的模糊多类支持向量机算法FCS-SVM。在算法中,重构了优化问题及其约束条件,以及Lagrange公式,并进行了推导。通过在标准数据集上的几个实验,对这些算法进行了比较分析。实验结果表明提出的算法可以得到比较理想的分类精度。     

基于分类器的图像模糊边缘检测快速算法

通过对Pal King边缘检测算法的分析,提出了一种新的模糊边缘检测快速算法。首先对图像进行模糊增强,然后依据当前像素及其8-邻域像素的灰度,设计了一个分类器,通过计算相对于该分类器的模糊隶属度函数值,对像素进行边缘分类;最后锐化所得的边缘像素,剔除噪声。算法抛弃了Pal King方法中复杂的迭代运算,同时也克服了Pal King算法中对图像低灰度值边缘信息的丢失,还可以通过设置不同的参数来检测不同细节的边缘。实验结果表明,该快速算法比Pal King算法的边缘检测能力更强,同时运算速度提高了约20倍。     

基于表格查寻学习算法的自适应模糊分类器

以手写体数字识别问题为背景,提出了一种基于表格查寻学习算法的自适应模糊分类 器,并用Matlab给出了自适应模糊分类器的实现,进而对其进行了仿真。仿真结果表明,该自适应模 糊分类器在手写体数字识别的识别性能、利用语言信息、计算复杂性等方面均优于采用BP算法的三 层前馈分类器,体现了自适应模糊处理技术用于模式识别的优越性和潜力。