基于VISIT算法设计模糊分类器的进化方法

介绍了在没有数据分布先验知识的情况下，用进化方法直接从训练数据中建立紧致模糊分类系统的方法。使用VISIT算法获取每个个体模糊系统，再用遗传算法从中搜索最优的模糊系统。规则和隶属函数是在进化过程中自动建立和优化的。为了同时有效地评价系统的精度和紧致性，用一个模糊专家系统作适应度函数。在2个基准分类问题上的实验结果表明了新方法的有效性。     

Power quality time series data mining using S-transform and fuzzy expert system

This paper presents a new approach for power quality time series data mining using S-transform based fuzzy expert system (FES). Initially the power signal time series disturbance data are pre-processed through an advanced signal processing tool such as S-transform and various statistical features are extracted, which are used as inputs to the fuzzy expert system for power quality event detection. The proposed expert system uses a data mining approach for assigning a certainty factor for each classification rule, thereby providing robustness to the rule in the presence of noise. Further to provide a very high degree of accuracy in pattern classification, both the Gaussian and trapezoidal membership functions of the concerned fuzzy sets are optimized using a fuzzy logic based adaptive particle swarm optimization (PSO) technique. The proposed hybrid PSO-fuzzy expert system (PSOFES) provides accurate classification rates even under noisy conditions compared to the existing techniques, which show the efficacy and robustness of the proposed algorithm for power quality time series data mining.     

A fuzzy genetic algorithm for the discovery of process parameter settings using knowledge representation

In this paper, we propose a fuzzy genetic algorithm (Fuzzy-GA) approach integrating fuzzy rule sets and their membership function sets, in a chromosome. The proposed approach consists of two processes: knowledge representation and knowledge assimilation. The knowledge of process parameter setting is encoded as a string with a fuzzy rule set and the associated membership functions. The historical process data forming a combined string is used as the initial knowledge population, which is then ready for knowledge assimilation. A genetic algorithm is used to generate an optimal or nearly optimal fuzzy set and membership functions for the process parameters. The originality of this research is that the proposed system is equipped with the ability to take advantage of assessing the loss which is caused by discrepancy with a process target, thereby enabling the identification of the best set of process parameters. The approach is demonstrated by the use of an experimental example drawn from a semiconductor manufacturer and the results show us that the suggested approach is able to achieve an optimal solution for a process parameter setting problem.     

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.     

Genetic algorithm in designing fuzzy information retrieval-based classifier by principal component analysis

The aim of this paper is to develop a fuzzy classifier form the point of view of a fuzzy information retrieval system. The genetic algorithm is employed to find useful fuzzy concepts with high classification performance for classification problems; then, each of classes and patterns can be represented by a fuzzy set of useful fuzzy concepts. Each of fuzzy concepts is linguistically interpreted and the corresponding membership functions remain fixed during the evolution. A pattern can be categorized into one class if there exists a maximum degree of similarity between them. For not distorting the usefulness of the proposed classifier for high-dimensional problems, the principal component analysis is incorporated into the proposed classifier to reduce dimensions. The generalization ability of the proposed classifier is examined by performing computer simulations on some well-known data sets, such as the breast cancer data and the wine classification data. The results demonstrate that the proposed classifier works well in comparison with other classification methods.     

基于演进向量量化聚类的增量模糊关联分类方法

为了提高动态数据集上模糊关联分类器（FAC）的建模效率,提出了一种基于演进向量量化（eVQ）聚类的增量模糊关联分类方法。首先,采用eVQ聚类算法增量更新数量属性上的高斯隶属度函数参数;然后,扩展早剪枝更新（UWEP）算法,使之适用于增量挖掘模糊频繁项;最后,以模糊相关度（FCORR）和分类规则前件长度为度量方式裁剪并更新模糊关联分类规则库。在4个UCI标准数据集上的实验结果表明,与批量模糊关联分类建模方法相比,所提方法能够在保证分类精度和解释性的前提下,减少模糊关联分类器的训练时间;基于eVQ的高斯隶属度函数的增量更新有助于提高动态数据集上模糊关联分类器的分类精度。     

模糊树模型及其在复杂系统辨识中的应用

基于二叉树和模糊逻辑理论,提出了一种用于复杂系统建模的模糊树模型.将线性 模型和模糊集组织在树结构上,并给出了更新线性模型系数和模糊集隶属度函数的混合算 法.与其他建模方法相比,如ANFIS,模糊树模型计算量小,精度高,尤其在高维数据建模中 更为明显.仿真结果描述了这种方法的性能.     

AGFS: Adaptive Genetic Fuzzy System for medical data classification

A Genetic Fuzzy System (GFS) is basically a fuzzy system augmented by a learning process based on a genetic algorithm (GA). Fuzzy systems have demonstrated their ability to solve different kinds of problems in various application domains. Currently, there is an increasing interest to augment fuzzy systems with learning and adaptation capabilities. Two of the most successful approaches to hybridize fuzzy systems with learning and adaptation methods have been made in the realm of soft computing. The GA can be merged with Fuzzy system for different purposes like rule selection, membership function optimization, rule generation, co-efficient optimization, for data classification. Here we propose an Adaptive Genetic Fuzzy System (AGFS) for optimizing rules and membership functions for medical data classification process. The primary intension of the research is 1) Generating rules from data as well as for the optimized rules selection, adapting of genetic algorithm is done and to explain the exploration problem in genetic algorithm, introduction of new operator, called systematic addition is done, 2) Proposing a simple technique for scheming of membership function and Discretization, and 3) Designing a fitness function by allowing the frequency of occurrence of the rules in the training data. Finally, to establish the efficiency of the proposed classifier the presentation of the anticipated genetic-fuzzy classifier is evaluated with quantitative, qualitative and comparative analysis. From the outcome, AGFS obtained better accuracy when compared to the existing systems.     

A multi-objective genetic optimization of interpretability-oriented fuzzy rule-based classifiers

The paper presents a multi-objective genetic approach to design interpretability-oriented fuzzy rule-based classifiers from data. The proposed approach allows us to obtain systems with various levels of compromise between their accuracy and interpretability. During the learning process, parameters of the membership functions, as well as the structure of the classifier's fuzzy rule base (i.e., the number of rules, the number of rule antecedents, etc.) evolve simultaneously using a Pittsburgh-type genetic approach. Since there is no particular coding of fuzzy rule structures in a chromosome (it reduces computational complexity of the algorithm), original crossover and mutation operators, as well as chromosome-repairing technique to directly transform the rules are also proposed. To evaluate both the accuracy and interpretability of the system, two measures are used. The first one – an accuracy measure – is based on the root mean square error of the system's response. The second one – an interpretability measure – is based on the arithmetic mean of three components: (a) the average length of rules (the average number of antecedents used in the rules), (b) the number of active fuzzy sets and (c) the number of active inputs of the system (an active fuzzy set or input means a set or input used by at least one fuzzy rule). Both measures are used as objectives in multi-objective (2-objective in our case) genetic optimization approaches such as well-known SPEA2 and NSGA-II algorithms. Moreover, for the purpose of comparison with several alternative approaches, the experiments are carried out both considering the so-called strong fuzzy partitions (SFPs) of attribute domains and without them. SFPs provide more semantically meaningful solutions, usually at the expense of their accuracy. The operation of the proposed technique in various classification problems is tested with the use of 20 benchmark data sets and compared to 11 alternative classification techniques. The experiments show that the proposed approach generates classifiers of significantly improved interpretability, while still characterized by competitive accuracy.     

A Fuzzy Bayesian Classifier with Learned Mahalanobis Distance

Recent developments show that naive Bayesian classifier (NBC) performs significantly better in applications, although it is based on the assumption that all attributes are independent of each other. However, in the NBC each variable has a finite number of values, which means that in large data sets NBC may not be so effective in classifications. For example, variables may take continuous values. To overcome this issue, many researchers used fuzzy naive Bayesian classification for partitioning the continuous values. On the other hand, the choice of the distance function is an important subject that should be taken into consideration in fuzzy partitioning or clustering. In this study, a new fuzzy Bayes classifier is proposed for numerical attributes without the independency assumption. To get high accuracy in classification, membership functions are constructed by using the fuzzy C‐means clustering (FCM). The main objective of using FCM is to obtain membership functions directly from the data set instead of consulting to an expert. The proposed method is demonstrated on the basis of two well‐known data sets from the literature, which consist of numerical attributes only. The results show that the proposed the fuzzy Bayes classification is at least comparable to other methods.     

Designing of classifiers based on immune principles and fuzzy rules

This paper proposed an algorithm to design a fuzzy classification system based on immune principles. The proposed algorithm evolves a population of antibodies based on the clonal selection and hypermutation principles. The membership function parameters and the fuzzy rule set including the number of rules inside it are evolved at the same time. Each antibody (candidate solution) corresponds to a fuzzy classification rule set. We compared our algorithm with other classification schemes on some benchmark datasets. The results demonstrated the effectiveness of the proposed immune algorithm.     

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.     

Hydraulic turbine governing system identification using T–S fuzzy model optimized by chaotic gravitational search algorithm

Hydraulic turbine governing system (HTGS) is a complicated nonlinear system that controls the frequency and power output of hydroelectric generating unit (HGU). The modeling of HTGS is an important and difficult task, because some components, like hydraulic turbine and governor actuator, are with strong nonlinearity. In this paper, a novel Takagi–Sugeno (T–S) fuzzy model identification method based on chaotic gravitational search algorithm (CGSA) is proposed and applied in the modeling of HTGS. In the proposed method, fuzzy c-regression model clustering algorithm is used to partition the input space and identify the coarse antecedent membership function (MF) parameters at first. And then, a novel CGSA is proposed to search better MF parameters around the coarse results, in which chaotic search has been embedded in the iteration of basic GSA to search and replace the current best solution of GSA. The performance of the proposed fuzzy model identification method is validated by benchmark problems, and the results show that the accuracies of identified models have been improved significantly compared with the other existing models. Finally, the proposed approach has been applied to approximate the dynamic behaviors of HTGS of a HGU in a hydropower station of Jiangxi Province of China. The experimental results show that our approach can identify the HTGS satisfactorily with acceptable accuracy.     

Learning Premises of Fuzzy Rules for Knowledge Acquisition in Classification Problems

A key issue in building fuzzy classification systems is the specification of rule conditions, which determine the structure of a knowledge base. This paper presents a new approach to automatically extract classification knowledge from numerical data by means of premise learning. A genetic algorithm is employed to search for premise structure in combination with parameters of membership functions of input fuzzy sets to yield optimal conditions of classification rules. The major advantage of our work is that a parsimonious knowledge base with a low number of rules can be achieved. The practical applicability of the proposed method is examined by computer simulations on two well-known benchmark problems of Iris Data and Cancer Data classification. Received 11 February 1999 / Revised 13 January 2001 / Accepted in revised form 13 February 2001     

Fuzzy system reliability evaluation using time-dependent intuitionistic fuzzy set

In general, fuzzy sets are used to analyse the system reliability. In this article, the concept of fuzzy set is extended by the idea of intuitionistic fuzzy set (IFS) and a new general procedure is proposed to construct the membership and non-membership functions of the fuzzy reliability using time-dependent IFS. Here, failure rate function of the system is represented by a triangular intuitionistic fuzzy number (IFN). Also, using proposed approach, membership and non-membership functions of fuzzy reliability of series and parallel systems are constructed, where the failure rate of each component is taken as a time-dependent triangular IFN. The major advantage of using IFS over fuzzy sets is that IFS separate the positive and negative evidences for membership of an element in the set. Numerical examples are given to illustrate the proposed approach.     

Attribute selection based on information gain ratio in fuzzy rough set theory with application to tumor classification

Tumor classification based on gene expression levels is important for tumor diagnosis. Since tumor data in gene expression contain thousands of attributes, attribute selection for tumor data in gene expression becomes a key point for tumor classification. Inspired by the concept of gain ratio in decision tree theory, an attribute selection method based on fuzzy gain ratio under the framework of fuzzy rough set theory is proposed. The approach is compared to several other approaches on three real world tumor data sets in gene expression. Results show that the proposed method is effective. This work may supply an optional strategy for dealing with tumor data in gene expression or other applications.     

Predictive modular fuzzy systems for time-series classification

We introduce the so-called predictive modular fuzzy system (PREMOFS) which performs time-series classification. A PREMOFS consists of 1) a bank of prediction modules and 2) a fuzzy decision module. It is assumed that the time series is generated by a source belonging to a finite search set (universal set); then the classification problem is to select the source that best represents the observed data, Classification is based on a membership function which is updated recursively according to the predictive accuracy of each model. Two algorithms are presented for updating the membership function. The first is based on sum/product fuzzy inference and the second on max/min fuzzy inference. In short, PREMOFS is a fuzzy modular system that classifies time series to one of a finite number of classes using the full set of past data (without preprocessing) to perform a recursive competitive computation of membership function based on predictive accuracy. Convergence proofs are given for both PREMOFS algorithms; in both cases the membership grade tends to one for the source that best predicts the observed data and to less than one for the remaining sources; hence, correct classification is guaranteed. Simulation results are also presented: PREMOFS are applied to signal detection, system identification, and phoneme classification tasks     

A fuzzy approach to partitioning continuous attributes for classification

Classification is an important topic in data mining research. To better handle continuous data, fuzzy sets are used to represent interval events in the domains of continuous attributes, allowing continuous data lying on the interval boundaries to partially belong to multiple intervals. Since the membership functions of fuzzy sets can profoundly affect the performance of the models or rules discovered, the determination of membership functions or fuzzy partitioning is crucial. In this paper, we present a new method to determine the membership functions of fuzzy sets directly from data to maximize the class-attribute interdependence and, hence, improve the classification results. In other words, it forms a fuzzy partition of the input space automatically, using an information-theoretic measure to evaluate the interdependence between the class membership and an attribute as the objective function for fuzzy partitioning. To find the optimum of the measure, it employs fractional programming. To evaluate the effectiveness of the proposed method, several real-world data sets are used in our experiments. The experimental results show that this method outperforms other well-known discretization and fuzzy partitioning approaches.     

基于加权模糊隶属度的二叉树多分类算法

针对二叉树支持向量机多分类算法准确率与分类效率较低的问题,提出了一种基于加权模糊隶属度的二叉树支持向量机多分类算法（binary tree support vector machines multi-classification algorithm based on weighted fuzzy membership,PF-BTSVM）。该算法依据最大最小样本距离与质心距离构造出一个近似完全二叉树,提高了整体结构的分类效率;利用模糊隶属度函数以及正负辅助惩罚因子对训练集进行筛选,剔除掉对分类无用的样本与噪声值,实现了训练集的提纯并且削弱了不平衡分类时超平面的偏移。在数据集上的实验结果表明,与其他二叉树多分类算法相比,该算法在提高了分类准确率以及稳定性的的同时还加快了训练与分类的速度,而且这种优势当分类的不平衡度越大时越明显。     

Fuzzy SVM with a New Fuzzy Membership Function to Solve the Two-Class Problems

In dealing with the Two-Class classification problems, the traditional support vector machine (SVM) often cannot achieve good classification accuracy when outliers exist in the training data set. The fuzzy support vector machine (FSVM) can resolve this problem with an appropriate fuzzy membership for each data point. The effect of the outliers can be effectively reduced when the classification problem is solved. In this paper, a new fuzzy membership function is employed in the linear and nonlinear fuzzy support vector machine respectively. The fuzzy membership is calculated based on the structural information of two classes in the input space and in the feature space. This method can distinguish the support vectors and the outliers effectively. Experimental results show that this approach contributes greatly to the reduction of the effect of the outliers and significantly improves the classification accuracy and generalization.