A new method for constructing membership functions and fuzzy rulesfrom training examples

To extract knowledge from a set of numerical data and build up a rule-based system is an important research topic in knowledge acquisition and expert systems. In recent years, many fuzzy systems that automatically generate fuzzy rules from numerical data have been proposed. In this paper, we propose a new fuzzy learning algorithm based on the alpha-cuts of equivalence relations and the alpha-cuts of fuzzy sets to construct the membership functions of the input variables and the output variables of fuzzy rules and to induce the fuzzy rules from the numerical training data set. Based on the proposed fuzzy learning algorithm, we also implemented a program on a Pentium PC using the MATLAB development tool to deal with the Iris data classification problem. The experimental results show that the proposed fuzzy learning algorithm has a higher average classification ratio and can generate fewer rules than the existing algorithm.     

A NEW METHOD TO GENERATE FUZZY RULES FROM TRAINING INSTANCES FOR HANDLING CLASSIFICATION PROBLEMS

A major task in developing a fuzzy classification system is to generate a set of fuzzy rules from training instances to deal with a specific classification problem. In recent years, many methods have been developed to generate fuzzy rules from training instances. We present a new method to generate fuzzy rules from training instances to deal with the Iris data classification problem. The proposed method can discard some useless input attributes to improve the average classification accuracy rate. It can obtain a higher average classification accuracy rate and it generates fewer fuzzy rules and fewer input fuzzy sets in the generated fuzzy rules than the existing methods.     

AUTOMATICALLY CONSTRUCTING MEMBERSHIP FUNCTIONS AND GENERATING FUZZY RULES USING GENETIC ALGORITHMS

The most important task in designing a fuzzy classification system is to find a set of fuzzy rules from training data to deal with a specific classification problem. In recent years, many methods have been proposed to construct membership functions and generate fuzzy rules from training data for handling fuzzy classification problems. We propose a new method to generate fuzzy rules from training data by using genetic algorithms (GAs). First, we divide the training data into several clusters by using the weighted distance clustering method and generate a fuzzy rule for each cluster. Then, we use GAs to tune the membership functions of the generated fuzzy rules. The proposed method attains a higher average classification accuracy rate than the existing methods.     

Mining fuzzy association rules for classification problems

The effective development of data mining techniques for the discovery of knowledge from training samples for classification problems in industrial engineering is necessary in applications, such as group technology. This paper proposes a learning algorithm, which can be viewed as a knowledge acquisition tool, to effectively discover fuzzy association rules for classification problems. The consequence part of each rule is one class label. The proposed learning algorithm consists of two phases: one to generate large fuzzy grids from training samples by fuzzy partitioning in each attribute, and the other to generate fuzzy association rules for classification problems by large fuzzy grids. The proposed learning algorithm is implemented by scanning training samples stored in a database only once and applying a sequence of Boolean operations to generate fuzzy grids and fuzzy rules; therefore, it can be easily extended to discover other types of fuzzy association rules. The simulation results from the iris data demonstrate that the proposed learning algorithm can effectively derive fuzzy association rules for classification problems.     

一种使用启发式搜索优化的模糊规则分类方法

文章提出了一种基于模糊规则的分类方法。该方法首先介绍了基于模糊C均值聚类的模糊规则提取,然后利用所建立的模糊规则库设计了一种分类算法,并且利用启发式搜索来精简分类规则。使用IRIS数据对该文的方法进行了性能测试,结果表明该方法在训练样本较少的情况下,能得到很好的分类效果,并且通过规则精简,所使用的规则数目大大下降,而分类性能更加优良。     

一种基于模糊规则的分类方法

本文提出了一种基于模糊规则的分类方法。首先介绍了一种新的模糊规则提取方法，然后基于所提取的模糊规则给出了一个采用二级判决的分类算法，并利用IRIS数据对此分类算法进行了仿真测试。结果表明，该算法在训练样本较少的情况下，仍能得到很好的分类效果.     

A NEW METHOD TO GENERATE FUZZY RULES FROM RELATIONAL DATABASE SYSTEMS FOR ESTIMATING NULL VALUES

Fuzzy decision trees can be used to generate fuzzy rules from training instances to deal with forecasting and classification problems. We propose a new method to construct fuzzy decision trees from relational database systems and to generate fuzzy rules from the constructed fuzzy decision trees for estimating null values, where the weights of attributes are used to derive the values of certainty factors of the generated fuzzy rules. We use the concept of "coefficient of determination" of the statistics to derive the weights of the attributes in relational database systems and use the normalized weights of the attributes to derive the values of certainty factors of the generated fuzzy rules. Furthermore, we also use regression equations of the statistics to construct a complete fuzzy decision tree for generating better fuzzy rules. The proposed method obtains a higher average estimated accuracy rate than the existing methods for estimating null values in relational database systems.     

一种模糊规则提取方法的研究

提出了一种基于改进的模糊 C 均值聚类的模糊规则提取方法。然后基于所提取的模糊规则给出了一种分类算法,并利用 IRIS 数据对此分类算法进行了仿真测试。结果表明,该算法在训练祥本较少的情况下,仍能得到很好的分类效果,由此说明所提出的模糊规则生成方法有效。     

Elicitation of classification rules by fuzzy data mining

Data mining techniques can be used to find potentially useful patterns from data and to ease the knowledge acquisition bottleneck in building prototype rule-based systems. Based on the partition methods presented in simple-fuzzy-partition-based method (SFPBM) proposed by Hu et al. (Comput. Ind. Eng. 43(4) (2002) 735), the aim of this paper is to propose a new fuzzy data mining technique consisting of two phases to find fuzzy if–then rules for classification problems: one to find frequent fuzzy grids by using a pre-specified simple fuzzy partition method to divide each quantitative attribute, and the other to generate fuzzy classification rules from frequent fuzzy grids. To improve the classification performance of the proposed method, we specially incorporate adaptive rules proposed by Nozaki et al. (IEEE Trans. Fuzzy Syst. 4(3) (1996) 238) into our methods to adjust the confidence of each classification rule. For classification generalization ability, the simulation results from the iris data demonstrate that the proposed method may effectively derive fuzzy classification rules from training samples.     

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.     

Design of adaptive fuzzy model for classification problem

The main theme of this paper is to set up an adaptive fuzzy model for a new classification problem. At first, we propose a fuzzy classification model that can automatically generate the fuzzy IF-THEN rules by the features of the training database. The consequent part of the fuzzy IF-THEN rule consists of the confident value of the rule and which class the datum should belong to. Then a novel adaptive modification algorithm (AMA) is developed to tune the confident value of the fuzzy classification model. The proposed model comprises three modules, generation of the fuzzy IF-THEN rules, determination of the classification unit, and setup of the AMA. Computer simulations on the well known Wine and Iris databases have tested the performance. Simulations demonstrate that the proposed method can provide sufficiently high classification rate in comparison with other fuzzy classification models.     

Fuzzy rules extraction from support vector machines for multi-class classification

This paper proposes a new method for fuzzy rule extraction from trained support vector machines (SVMs) for multi-class problems, named FREx_SVM. SVMs have been used in a variety of applications. However, they are considered “black box models,” where no interpretation about the input–output mapping is provided. Some methods to reduce this limitation have already been proposed, but they are restricted to binary classification problems and to the extraction of symbolic rules with intervals or functions in their antecedents. In order to improve the interpretability of the generated rules, this paper presents a new model for extracting fuzzy rules from a trained SVM. The proposed model is suited for classification in multi-class problems and includes a wrapper feature selection algorithm. It is evaluated in four benchmark databases, and results obtained demonstrate its capacity to generate a reduced set of interpretable fuzzy rules that explains both the classification database and the influence of each input variable on the determination of the final class.     

Neuro-fuzzy learning with symbolic and numeric data

In real world datasets we often have to deal with different kinds of variables. The data can be, for example, symbolic or numeric. Data analysis methods can often deal with only one kind of data. Even when fuzzy systems are applied – which are not dependent on the scales of variables – usually only numeric data is considered. In this paper we present learning algorithms for creating fuzzy rules and training membership functions from data with symbolic and numeric variables. The algorithms are exentions to our neuro-fuzzy classification approach NEFCLASS. We also demonstrate the applicability of the algorithms on two real-world datasets.     

Rough set feature selection and rule induction for prediction of malignancy degree in brain glioma

The degree of malignancy in brain glioma is assessed based on magnetic resonance imaging (MRI) findings and clinical data before operation. These data contain irrelevant features, while uncertainties and missing values also exist. Rough set theory can deal with vagueness and uncertainty in data analysis, and can efficiently remove redundant information. In this paper, a rough set method is applied to predict the degree of malignancy. As feature selection can improve the classification accuracy effectively, rough set feature selection algorithms are employed to select features. The selected feature subsets are used to generate decision rules for the classification task. A rough set attribute reduction algorithm that employs a search method based on particle swarm optimization (PSO) is proposed in this paper and compared with other rough set reduction algorithms. Experimental results show that reducts found by the proposed algorithm are more efficient and can generate decision rules with better classification performance. The rough set rule-based method can achieve higher classification accuracy than other intelligent analysis methods such as neural networks, decision trees and a fuzzy rule extraction algorithm based on Fuzzy Min-Max Neural Networks (FRE-FMMNN). Moreover, the decision rules induced by rough set rule induction algorithm can reveal regular and interpretable patterns of the relations between glioma MRI features and the degree of malignancy, which are helpful for medical experts.     

一种基于模糊关联分类的遥感图像分类方法

遥感图像分类是遥感领域的研究热点之一.提出了一种基于自适应区间划分的模糊关联遥感图像分类方法(fuzzy associative remote sensing classification,FARSC).算法根据遥感图像分类的特点,利用模糊C均值聚类算法自适应地建立连续型属性模糊区间,使用新的剪枝策略对项集进行筛选从而避免生成无用规则,采用一种新的规则重要性度量方法对多模糊分类规则进行融合,从而有效地提高分类效率和精确度.在UCI数据和遥感图像上所作实验结果表明,算法具有较高的分类精度以及对样本数量变化的不敏感性,对于解决遥感图像分类问题,FARSC算法具有较高的实用性,是一种有效的遥感图像分类方法.     

Fuzzy clustering-based discretization for gene expression classification

This paper presents a novel classification approach that integrates fuzzy class association rules and support vector machines. A fuzzy discretization technique based on fuzzy c-means clustering algorithm is employed to transform the training set, particularly quantitative attributes, to a format appropriate for association rule mining. A hill-climbing procedure is adapted for automatic thresholds adjustment and fuzzy class association rules are mined accordingly. The compatibility between the generated rules and fuzzy patterns is considered to construct a set of feature vectors, which are used to generate a classifier. The reported test results show that compatibility rule-based feature vectors present a highly- qualified source of discrimination knowledge that can substantially impact the prediction power of the final classifier. In order to evaluate the applicability of the proposed method to a variety of domains, it is also utilized for the popular task of gene expression classification. Further, we show how this method provide biologists with an accurate and more understandable classifier model compared to other machine learning techniques.     

A parsimony fuzzy rule-based classifier using axiomatic fuzzy set theory and support vector machines

This paper proposes a classification method that is based on easily interpretable fuzzy rules and fully capitalizes on the two key technologies, namely pruning the outliers in the training data by SVMs (support vector machines), i.e., eliminating the influence of outliers on the learning process; finding a fuzzy set with sound linguistic interpretation to describe each class based on AFS (axiomatic fuzzy set) theory. Compared with other fuzzy rule-based methods, the proposed models are usually more compact and easily understandable for the users since each class is described by much fewer rules. The proposed method also comes with two other advantages, namely, each rule obtained from the proposed algorithm is simply a conjunction of some linguistic terms, there are no parameters that are required to be tuned. The proposed classification method is compared with the previously published fuzzy rule-based classifiers by testing them on 16 UCI data sets. The results show that the fuzzy rule-based classifier presented in this paper, offers a compact, understandable and accurate classification scheme. A balance is achieved between the interpretability and the accuracy.     

Fuzzy DIFACONN-miner: A novel approach for fuzzy rule extraction from neural networks

Artificial neural networks (ANNs) are mathematical models inspired from the biological nervous system. They have the ability of predicting, learning from experiences and generalizing from previous examples. An important drawback of ANNs is their very limited explanation capability, mainly due to the fact that knowledge embedded within ANNs is distributed over the activations and the connection weights. Therefore, one of the main challenges in the recent decades is to extract classification rules from ANNs. This paper presents a novel approach to extract fuzzy classification rules (FCR) from ANNs because of the fact that fuzzy rules are more interpretable and cope better with pervasive uncertainty and vagueness with respect to crisp rules. A soft computing based algorithm is developed to generate fuzzy rules based on a data mining tool (DIFACONN-miner), which was recently developed by the authors. Fuzzy DIFACONN-miner algorithm can extract fuzzy classification rules from datasets containing both categorical and continuous attributes. Experimental research on the benchmark datasets and comparisons with other fuzzy rule based classification (FRBC) algorithms has shown that the proposed algorithm yields high classification accuracies and comprehensible rule sets.     

Quantum Fuzzy Support Vector Machine for Binary Classification

In the objective world, how to deal with the complexity and uncertainty of big data efficiently and accurately has become the premise and key to machine learning. Fuzzy support vector machine (FSVM) not only deals with the classification problems for training samples with fuzzy information, but also assigns a fuzzy membership degree to each training sample, allowing different training samples to contribute differently in predicting an optimal hyperplane to separate two classes with maximum margin, reducing the effect of outliers and noise, Quantum computing has super parallel computing capabilities and holds the promise of faster algorithmic processing of data. However, FSVM and quantum computing are incapable of dealing with the complexity and uncertainty of big data in an efficient and accurate manner. This paper research and propose an efficient and accurate quantum fuzzy support vector machine (QFSVM) algorithm based on the fact that quantum computing can efficiently process large amounts of data and FSVM is easy to deal with the complexity and uncertainty problems. The central idea of the proposed algorithm is to use the quantum algorithm for solving linear systems of equations (HHL algorithm) and the least-squares method to solve the quadratic programming problem in the FSVM. The proposed algorithm can determine whether a sample belongs to the positive or negative class while also achieving a good generalization performance. Furthermore, this paper applies QFSVM to handwritten character recognition and demonstrates that QFSVM can be run on quantum computers, and achieve accurate classification of handwritten characters. When compared to FSVM, QFSVM’s computational complexity decreases exponentially with the number of training samples.