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.     

Robust fuzzy relational classifier incorporating the soft class labels

Fuzzy relational classifier (FRC) is a recently proposed two-step nonlinear classifier. At first, the unsupervised fuzzy c-means (FCM) clustering is performed to explore the underlying groups of the given dataset. Then, a fuzzy relation matrix indicating the relationship between the formed groups and the given classes is constructed for subsequent classification. It has been shown that FRC has two advantages: interpretable classification results and avoidance of overtraining. However, FRC not only lacks the robustness which is very important for a classifier, but also fails on the dataset with non-spherical distributions. Moreover, the classification mechanism of FRC is sensitive to the improper class labels of the training samples, thus leading to considerable decline in classification performance. The purpose of this paper is to develop a Robust FRC (RFRC) algorithm aiming at overcoming or mitigating all of the above disadvantages of FRC and maintaining its original advantages. In the proposed RFRC algorithm, we employ our previously proposed robust kernelized FCM (KFCM) to replace FCM to enhance its robustness against outliers and its suitability for the non-spherical data structures. In addition, we incorporate the soft class labels into the classification mechanism to improve its performance, especially for the datasets containing the improper class labels. The experimental results on 2 artificial and 11 real-life benchmark datasets demonstrate that RFRC algorithm can consistently outperform FRC in classification performance.     

基于模糊分类关联规则的支持向量机分类器生成方法

为提高数据库分类系统的分类精度,提出一种新的分类方法。首先,利用模糊C-均值聚类算法对数据库中的连续属性进行离散化;然后,在此基础上提出一种改进的模糊关联算法挖掘分类关联规则;最后,通过计算规则和模式之间的兼容性指标来构造特征向量,构建支持向量机的分类器模型。实验结果表明,该方法具有较高的分类识别能力和分类效率。     

Effects of constructing fuzzy discretization from crisp discretization for rule-based classifiers

Crisp discretization is one of the most widely used methods for handling continuous attributes. In crisp discretization, each attribute is split into several intervals and handled as discrete numbers. Although crisp discretization is a convenient tool, it is not appropriate in some situations (e.g., when there is no clear boundary and we cannot set a clear threshold). To address such a problem, several discretizations with fuzzy sets have been proposed. In this paper we examine the effect of fuzzy discretization derived from crisp discretization. The fuzziness of fuzzy discretization is controlled by a fuzzification grade F. We examine two procedures for the setting of F. In one procedure, we set F beforehand and do not change it through training rule-based classifiers. In the other procedure, first we set F and then change it after training. Through computational experiments, we show that the accuracy of rule-based classifiers is improved by an appropriate setting of the grade of fuzzification. Moreover, we show that increasing the grade of fuzzification after training classifiers can often improve generalization ability. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Fusion of images interpreted by a new fuzzy classifier

This paper presents a global system for the fusion of images segmented by various methods and interpreted by a fuzzy classifier. A set of complementary segmentation operators is applied to the image. Each region of the segmented images is interpreted by the fuzzy classifier, through membership degrees to classes. The fuzzy classifier builds the classes automatically from examples, even in the case of complex data sets. Interpreted images are then merged by a fusion operator from the fuzzy set theory. Several fusion operators are compared. They trust more high membership degrees to classes, which are considered as reliability degrees. The fusion of the interpreted images improves the segmentation, and gives solutions to segmentation and interpretation evaluation.     

A fuzzy classifier to deal with similarity between labels on automatic prosodic labeling

This paper presents an original approach to automatic prosodic labeling. Fuzzy logic techniques are used for representing situations of high uncertainty with respect to the category to be assigned to a given prosodic unit. The Fuzzy Integer technique is used to combine the output of different base classifiers. The resulting fuzzy classifier benefits from the different capabilities of the base classifiers for identifying different types of prosodic events. At the same time, the fuzzy classifier identifies the events that are potentially more difficult to be labeled. The classifier has been applied to the identification of ToBI pitch accents. The state of the art on pitch accent multiclass classification reports around 70% accuracy rate. In this paper we describe a fuzzy classifier which assigns more than one label in confusing situations. We show that the pairs of labels that appear in these uncertain situations are consistent with the most confused pairs of labels reported in manual prosodic labeling experiments. Our fuzzy classifier obtains a soft classification rate of 81.8%, which supports the potential of the proposed system for computer assisted prosodic labeling.     

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.     

A general framework for designing a fuzzy rule-based classifier

This paper presents a general framework for designing a fuzzy rule-based classifier. Structure and parameters of the classifier are evolved through a two-stage genetic search. To reduce the search space, the classifier structure is constrained by a tree created using the evolving SOM tree algorithm. Salient input variables are specific for each fuzzy rule and are found during the genetic search process. It is shown through computer simulations of four real world problems that a large number of rules and input variables can be eliminated from the model without deteriorating the classification accuracy. By contrast, the classification accuracy of unseen data is increased due to the elimination.     

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.     

Design of fuzzy classifier for diabetes disease using Modified Artificial Bee Colony algorithm

In this study, diagnosis of diabetes disease, which is one of the most important diseases, is conducted with artificial intelligence techniques. We have proposed a novel Artificial Bee Colony (ABC) algorithm in which a mutation operator is added to an Artificial Bee Colony for improving its performance. When the current best solution cannot be updated, a blended crossover operator (BLX-α) of genetic algorithm is applied, in order to enhance the diversity of ABC, without compromising with the solution quality. This modified version of ABC is used as a new tool to create and optimize automatically the membership functions and rules base directly from data. We take the diabetes dataset used in our work from the UCI machine learning repository. The performances of the proposed method are evaluated through classification rate, sensitivity and specificity values using 10-fold cross-validation method. The obtained classification rate of our method is 84.21% and it is very promising when compared with the previous research in the literature for the same problem.     

基于直觉模糊聚类的数据关联算法

针对多传感器观测数据存在不确定性的问题,基于直觉模糊聚类,提出一种新的数据关联算法。将改进的直觉模糊C-均值聚类（IFCM）算法应用于数据关联,首先将观测数据和预测数据进行直觉模糊化,然后计算直觉模糊集之间的加权距离以获得观测与航迹的隶属度,最后依次搜索最大隶属度实现观测与航迹的关联。仿真实验表明,存在模糊观测数据情况下,算法能有效地进行数据关联。     

基于公理化模糊集语义图像层次关联规则分类器

为提高语义图像分类器性能,提出一种基于公理化模糊集的语义图像层次关联规则分类器。首先,为提高算法精度,在对图像数据集进行特征提取基础上,采用公理化理论（AFS）构建图像集模糊概念的AFS属性表达,提高图像集属性辨识度;其次,为提高算法计算效率,考虑采用层次结构关联规则,构建语义图像分类器,利用概念之间的本体信息,提高并行分类能力;最后,通过对算法参数及横向对比实验,显示所提算法具有较高的计算精度和计算效率。     

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.     

Fuzzy J-Means: a new heuristic for fuzzy clustering

A fuzzy clustering problem consists of assigning a set of patterns to a given number of clusters with respect to some criteria such that each of them may belong to more than one cluster with different degrees of membership. In order to solve it, we first propose a new local search heuristic, called Fuzzy J-Means, where the neighbourhood is defined by all possible centroid-to-pattern relocations. The “integer” solution is then moved to a continuous one by an alternate step, i.e., by finding centroids and membership degrees for all patterns and clusters. To alleviate the difficulty of being stuck in local minima of poor value, this local search is then embedded into the Variable Neighbourhood Search metaheuristic. Results on five standard test problems from the literature are reported and compared with those obtained with the well-known Fuzzy C-Means heuristic. It appears that solutions of substantially better quality are obtained with the proposed methods than with this former one.     

基于模糊聚类的模糊关联规则在流程企业中的应用

采用数据挖掘中的模糊聚类分析了流程企业中历史数据的区间值,然后用模糊关联规则挖掘出有用的规则。首先阐述了模糊聚类的RFCM算法和关联规则的Apriori算法的内容,分析了实现模糊关联规则的Fuzzy_ClustApriori算法流程,并用RFCM算法对实际数据进行分析,得到不同类别的模糊数。根据Fuzzy_ClustApriori算法的步骤对模糊化的参数点进行处理,得到了有价值的模糊规则,为流程企业的生产优化提供了理论依据。     

Extraction and optimization of fuzzy association rules using multi-objective genetic algorithm

Association Rule Mining is one of the important data mining activities and has received substantial attention in the literature. Association rule mining is a computationally and I/O intensive task. In this paper, we propose a solution approach for mining optimized fuzzy association rules of different orders. We also propose an approach to define membership functions for all the continuous attributes in a database by using clustering techniques. Although single objective genetic algorithms are used extensively, they degenerate the solution. In our approach, extraction and optimization of fuzzy association rules are done together using multi-objective genetic algorithm by considering the objectives such as fuzzy support, fuzzy confidence and rule length. The effectiveness of the proposed approach is tested using computer activity dataset to analyze the performance of a multi processor system and network audit data to detect anomaly based intrusions. Experiments show that the proposed method is efficient in many scenarios.

Novel associative classifier based on dynamic adaptive PSO: Application to determining candidates for thoracic surgery

Association rule mining is a data mining technique for discovering useful and novel patterns or relationships from databases. These rules are simple to infer and intuitive and can be easily used for classification in any domain that requires explanation for and investigation into how the classification works. Examples of such areas are medicine, agriculture, education, etc. For such a system to find wide adoptability, it should give output that is correct and comprehensible. The amount of data has been growing very fast and so has the search space of these problems. So we need to change traditional methods. This paper discusses a rule mining classifier called DA-AC (dynamic adaptive-associative classifier) which is based on a Dynamic Particle Swarm Optimizer. Due to its seeding method, exemplar selection, adaptive parameters, dynamic reconstruction of regions and velocity update, it avoids premature convergence and provides a better value in every dimension. Quality evaluation is done both for individual rules as well as entire rulesets. Experiments were conducted over fifteen benchmark datasets to evaluate performance of proposed algorithm in comparison with six other state-of-the-art non associative classifiers and eight associative classifiers. Results demonstrate competitive performance of proposed DA-AC while considering predictive accuracy and number of mined patterns as parameters. The method was then applied to predict life expectancy of post operative thoracic surgery patients.     

A multi-objective evolutionary method for learning granularities based on fuzzy discretization to improve the accuracy-complexity trade-off of fuzzy rule-based classification systems: D-MOFARC algorithm

Multi-objective evolutionary algorithms represent an effective tool to improve the accuracy-interpretability trade-off of fuzzy rule-based classification systems. To this aim, a tuning process and a rule selection process can be combined to obtain a set of solutions with different trade-offs between the accuracy and the compactness of models. Nevertheless, an initial model needs to be defined, in particular the parameters that describe the partitions and the number of fuzzy sets of each variable (i.e. the granularities) must be determined. The simplest approach is to use a previously established single granularity and a uniform fuzzy partition for each variable. A better approach consists in automatically identifying from data the appropriate granularities and fuzzy partitions, since this usually leads to more accurate models.This contribution presents a fuzzy discretization approach, which is used to generate automatically promising granularities and their associated fuzzy partitions. This mechanism is integrated within a Multi-Objective Fuzzy Association Rule-Based Classification method, namely D-MOFARC, which concurrently performs a tuning and a rule selection process on an initial knowledge base. The aim is to obtain fuzzy rule-based classification systems with high classification performances, while preserving their complexity.     

基于改进型模糊聚类的模糊系统建模方法

结合减法聚类和模糊C均值聚类,提出了一种改进型聚类算法,加快了收敛速度．利用改进后的算法对模糊系统输入或输出的样本集聚类,对聚类结果采用Trust-Region法拟合高斯型和S型函数,以实现模糊系统输入、输出空间的划分和隶属度函数参数的确定．结合MATLAB的模糊和曲线拟合工具箱,详述了如何在标准算法上进行改进和模糊系统建模．通过对IRIS标准数据聚类实验以及在解决机械加工误差复映问题上的应用,验证了改进后算法和建模方法的有效性．     

Design of fuzzy rule-based classifiers with semantic cointension

In computing with words (CWW), knowledge is linguistically represented and has an explicit semantics defined through fuzzy information granules. The linguistic representation, in turn, naturally bears an implicit semantics that belongs to users reading the knowledge base; hence a necessary condition for achieving interpretability requires that implicit and explicit semantics are cointensive. Interpretability is definitely stringent when knowledge must be acquired from data through inductive learning. Therefore, in this paper we propose a methodology for designing interpretable fuzzy models through semantic cointension. We focus our analysis on fuzzy rule-based classifiers (FRBCs), where we observe that rules resemble logical propositions, thus semantic cointension can be partially regarded as the fulfillment of the “logical view”, i.e. the set of basic logical laws that are required in any logical system. The proposed approach is grounded on the employment of a couple of tools: DCf, which extracts interpretable classification rules from data, and Espresso, that is capable of fast minimization of Boolean propositions. Our research demonstrates that it is possible to design models that exhibit good classification accuracy combined with high interpretability in the sense of semantic cointension. Also, structural parameters that quantify model complexity show that the derived models are also simple enough to be read and understood.