Evolutionary learning of rule premises for fuzzy modelling

The task of fuzzy modelling involves specification of rule antecedents and determination of their consequent counterparts. Rule premises appear here a critical issue since they determine the structure of a rule base. This paper proposes a new approach to extracting fuzzy rules from training examples by means of genetic-based premise learning. In order to construct a 'parsimonious' fuzzy model with high generalization ability, general premise structure allowing incomplete compositions of input variables as well as OR connectives of linguistic terms is considered. A genetic algorithm is utilized to optimize both the premise structure of rules and fuzzy set membership functions at the same time. Determination of rule conclusions is nested in the premise learning, where consequences of individual rules are determined under fixed preconditions. The proposed method was applied to the well-known gas furnace data of Box and Jenkins to show its validity and to compare its performance with those of other works.     

Adaptive Fuzzy Neural Networks as identifiers of discrete-time nonlinear dynamic systems

An adaptive supervised learning scheme is proposed in this paper for training Fuzzy Neural Networks (FNN) to identify discrete-time nonlinear dynamical systems. The FNN constructs are neural-network-based connectionist models consisting of several layers that are used to implement the functions of a fuzzy logic system. The fuzzy rule base considered here consists of Takagi-Sugeno IF-THEN rules, where the rule outputs are realized as linear polynomials of the input components. The FNN connectionist model is functionally partitioned into three separate parts, namely, the premise part, which provides the truth values of the rule preconditional statements, the consequent part providing the rule outputs, and the defuzzification part computing the final output of the FNN construct. The proposed learning scheme is a two-stage training algorithm that performs both structure and parameter learning, simultaneously. First, the structure learning task determines the proper fuzzy input partitions and the respective precondition matching, and is carried out by means of the rule base adaptation mechanism. The rule base adaptation mechanism is a self-organizing procedure which progressively generates the proper fuzzy rule base, during training, according to the operating conditions. Having completed the structure learning stage, the parameter learning is applied using the back-propagation algorithm, with the objective to adjust the premise/consequent parameters of the FNN so that the desired input/output representation is captured to an acceptable degree of accuracy. The structure/parameter training algorithm exhibits good learning and generalization capabilities as demonstrated via a series of simulation studies. Comparisons with conventional multilayer neural networks indicate the effectiveness of the proposed scheme.     

一种基于精简的模糊规则库的分类算法*

结合模糊聚类和粗糙集提出了一种基于精简的模糊规则库分类算法.对于数值型样本数据,首先采用模糊聚类生成模糊规则库,然后运用粗糙集理论对样本属性进行约简,删除冗余规则,即可得到精简的模糊规则库,以方便进行分类决策.通过对IRIS的仿真测试表明,本算法所产生的模糊规则不仅简单易懂,而且分类效果很好.     

复杂模糊分类系统的协同进化设计方法

提出一种基于协同进化算法的复杂模糊分类系统的设计方法．该方法由以下3步组成:1)利用Simba算法进行特征变量选择;2)采用模糊聚类算法辨识初始的模糊模型;3)利用协同进化算法对所获得的初始模糊模型进行结构和参数的优化．协同进化算法由三类种群组成;规则数种群,规则前件种群和隶属函数种群;其适应度函数同时考虑模型的精确性和解释性,采用三类种群合作计算的策略．利用该方法对多个典型问题进行分类,仿真结果验证了方法的有效性．     

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.     

SIGNIFICANT FUZZY RULES EXTRACTION BY AN SVD–QR-BASED APPROACH

ABSTRACT

In this article, an SVD–QR-based approach is proposed to extract the important fuzzy rules from a rule base with several fuzzy rule tables to design an appropriate fuzzy system directly from some input-output data of the identified system. A fuzzy system with fuzzy rule tables is defined to approach the input-output pairs of an identified system. In the rule base of the defined fuzzy system, each fuzzy rule table corresponds to a partition of an input space. In order to extract the important fuzzy rules from the rule base of the defined fuzzy system, a firing strength matrix determined by the membership functions of the premise fuzzy sets is constructed. According to the firing strength matrix, the number of important fuzzy rules is determined by the Singular Value Decomposition SVD, and the important fuzzy rules are selected by the SVD–QR-based method. Consequently, a reconstructed fuzzy rule base composed of significant fuzzy rules is determined by the firing strength matrix. Furthermore, the recursive least-squares method is applied to determine the consequent part of the reconstructed fuzzy system according to the gathered input-output data so that a fine fuzzy system is determined by the proposed method. Finally, three nonlinear systems illustrate the efficiency of the proposed method.     

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.     

Fuzzy rule generation for adaptive scheduling in a dynamic manufacturing environment

This paper proposes a fuzzy rule-based system for an adaptive scheduling, which dynamically selects and applies the most suitable strategy according to the current state of the scheduling environment. The adaptive scheduling problem is generally considered as a classification task since the performance of the adaptive scheduling system depends on the effectiveness of the mapping knowledge between system states and the best rules for the states. A rule base for this mapping is built and evolved by the proposed fuzzy dynamic learning classifier based on the training data cumulated by a simulation method. Distributed fuzzy sets approach, which uses multiple fuzzy numbers simultaneously, is adopted to recognize the system states. The developed fuzzy rules may readily be interpreted, adopted and, when necessary, modified by human experts. An application of the proposed method to a job-dispatching problem in a hypothetical flexible manufacturing system (FMS) shows that the method can develop more effective and robust rules than the traditional job-dispatching rules and a neural network approach.     

Checking the coherence and redundancy of fuzzy knowledge bases

Checking the coherence of a set of rules is an important step in knowledge base validation. Coherence is also needed in the field of fuzzy systems. Indeed, rules are often used regardless of their semantics, and it sometimes leads to sets of rules that make no sense. Avoiding redundancy is also of interest in real-time systems for which the inference engine is time consuming. A knowledge base is potentially inconsistent or incoherent if there exists a piece of input data that respects integrity constraints and that leads to logical inconsistency when added to the knowledge base. We more particularly consider knowledge bases composed of parallel fuzzy rules. Then, coherence means that the projection on the input variables of the conjunctive combination of the possibility distributions representing the fuzzy rules leaves these variables completely unrestricted (i.e., any value for these variables is possible) or, at least, not more restrictive than integrity constraints. Fuzzy rule representations can be implication-based or conjunction-based; we show that only implication-based models may lead to coherence problems. However, unlike conjunction-based models, they allow to design coherence checking processes. Some conditions that a set of parallel rules has to satisfy in order to avoid inconsistency problems are given for certainty or gradual rules. The problem of redundancy, which is also of interest for fuzzy knowledge bases validation, is addressed for these two kinds of rules     

一种新的模糊神经元网络学习方法

提出了一种模糊神经元网络的学习算法即利用多 层多层模糊IF/THEN规则表达专家知识的神经网络学习方法，在以此构造的基于多源信息融合的分类系统中，采用了多层模糊IF/THEN规则进行分类。为了处理模糊语言值，提出了一种能够控制模糊输入矢量的神经网络体系结构。该方法能够对非线性实间隔矢量和模糊矢量进行分类，工程实验表明，此学习算法是切实可行的。     

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.     

A Meteorological Fuzzy Expert System Incorporating Subjective User Input

We present a fuzzy expert system, MEDEX, for forecasting gale-force winds in the Mediterranean basin. The most successful local wind forecasting in this region is achieved by an expert human forecaster with access to numerical weather prediction products. That forecaster's knowledge is expressed as a set of ‘rules-of-thumb’. Fuzzy set methodologies have proved well suited for encoding the forecaster's knowledge, and for accommodating the uncertainty inherent in the specification of rules, as well as in subjective and objective input. MEDEX uses fuzzy set theory in two ways: as a fuzzy rule base in the expert system, and for fuzzy pattern matching to select dominant wind circulation patterns as one input to the expert system. The system was developed, tuned, and verified over a two-year period, during which the weather conditions from 539 days were individually analyzed. Evaluations of MEDEX performance for both the onset and cessation of winter and summer winds are presented, and demonstrate that MEDEX has forecasting skill competitive with the US Navy's regional forecasting center in Rota, Spain. Received 5 May 1999 / Revised 8 August 2000 / Accepted in revised form 23 April 2001     

基于数值型数据的模糊规则快速挖掘方法

针对数值型数据能准确反应现实世界，但难以理解的问题，为了从数值型数据中挖掘出易于理解的知识，提出了基于数值型数据的模糊规则快速挖掘方法。该方法能从数值型数据中挖掘出一个零阶的Sugeno模糊规则，并采用一种启发式方法将这个零阶的Sugeno模糊规则的数值结论转变为两个带置信度的语言变量，并给出了规则库的存储结构。最后通过实例证明了这种快速模糊规则挖掘方法能避免复杂的数值型计算和能有效逼近非线性函数的优点．     

Opening the black box of neural networks for remote sensing image classification

Neural networks, which make no assumption about data distribution, have achieved improved image classification results compared to traditional methods. Unfortunately, a neural network is generally perceived as being a ‘black box’. It is extremely difficult to document how specific classification decisions are reached. Fuzzy systems, on the other hand, have the capability to represent classification decisions explicitly in the form of fuzzy ‘if-then’ rules. However, the construction of a knowledge base, especially the fine-tuning of the fuzzy set parameters of the fuzzy rules in a fuzzy expert system, is a tedious and subjective process. This research has developed a new, improved neuro-fuzzy image classification system based on the synergism between neural networks and fuzzy expert systems. It incorporates the best of both technologies and compensates for the shortcomings of each. The learning algorithms of neural networks developed here are used to automate the derivation of fuzzy set parameters for the fuzzy ‘if-then’ rules in a fuzzy expert system. The rules obtained, in symbolic form, facilitate the understanding of the neural network based image classification system. In addition, the image classification accuracy obtained from the improved neuro-fuzzy system was significantly superior to those of the back-propagation based neural network and the maximum likelihood approaches.     

Symbolical Reasoning about Numerical Data: A Hybrid Approach

By combining methods from artificial intelligence and signal analysis, we have developed a hybrid system for medical diagnosis. The core of the system is a fuzzy expert system with a dual source knowledge base. Two sets of rules are acquired, automatically from given examples and indirectly formulated by the physician. A fuzzy neural network serves to learn from sample data and allows to extract fuzzy rules for the knowledge base. A complex signal transformation preprocesses the digital data a priori to the symbolic representation. Results demonstrate the high accuracy of the system in the field of diagnosing electroencephalograms where it outperforms the visual diagnosis by a human expert for some phenomena.     

Fuzzy rule-based similarity model enables learning from small case bases

The concept of similarity plays a fundamental role in case-based reasoning. However, the meaning of “similarity” can vary in situations and is largely domain dependent. This paper proposes a novel similarity model consisting of linguistic fuzzy rules as the knowledge container. We believe that fuzzy rules representation offers a more flexible means to express the knowledge and criteria for similarity assessment than traditional similarity metrics. The learning of fuzzy similarity rules is performed by exploiting the case base, which is utilized as a valuable resource with hidden knowledge for similarity learning. A sample of similarity is created from a pair of known cases in which the vicinity of case solutions reveals the similarity of case problems. We do pair-wise comparisons of cases in the case base to derive adequate training examples for learning fuzzy similarity rules. The empirical studies have demonstrated that the proposed approach is capable of discovering fuzzy similarity knowledge from a rather low number of cases, giving rise to the competence of CBR systems to work on a small case library.     

Using B-spline neural network to extract fuzzy rules for a centrifugal pump monitoring

In mechanical equipment monitoring tasks, fuzzy logic theory has been applied to situations where accurate mathematical models are unavailable or too complex to be established, but there may exist some obscure, subjective and empirical knowledge about the problem under investigation. Such kind of knowledge is usually formalized as a set of fuzzy relationships (rules) on which the entire fuzzy system is based upon. Sometimes, the fuzzy rules provided by human experts are only partial and rarely complete, while a set of system input/output data are available. Under such situations, it is desirable to extract fuzzy relationships from system data and combine human knowledge and experience to form a complete and relevant set of fuzzy rules. This paper describes application of B-spline neural network to monitor centrifugal pumps. A neuro-fuzzy approach has been established for extracting a set of fuzzy relationships from observation data, where B-spline neural network is employed to learn the internal mapping relations from a set of features/conditions of the pump. A general procedure has been setup using the basic structure and learning mechanism of the network and finally, the network performance and results have been discussed.     

基于GA和机器学习的启发式规则调度方法

采用基于遗传算法的启发式规则的新型调度方法来处理可变工艺路径的调度问题,同时建立起启发式调度规则库和用于选择规则的知识库,并利用机器学习和模糊推理机制进行样本与知识库的匹配,实现高效实用的调度。计算实例表明了该算法的优越性能     

Fuzzy expert system with double knowledge base for ultrasonic classification

This article shows a pattern recognition method for object classification using ultrasonic sensors and a dual knowledge base fuzzy expert system. The developed system uses a pair of ultrasonic sensors for obtaining information about the object shape from the ultrasonic echo signal envelope. In order to reduce the size of the database, a set of parameters is calculated for extracting knowledge about the object. However, the information provided by ultrasonic sensors contains a very high uncertainty level. This uncertainty is caused by several environmental effects, which are very difficult to eliminate in industrial applications. Among these environment factors are the air temperature and humidity, the air movement, etc. They create variations in the proprieties of the medium and disturbances during the acoustic propagation process. The presented system has been specially designed for industrial applications, where it is very difficult to reduce these disturbances and where it is necessary to use intelligent systems with high autonomy. The fuzzy expert system proposed has a dual knowledge base, that is, a statistical knowledge located on the memberships functions, and the standard rule-based knowledge. This expert system deals with the uncertainties in the information, and it is able to generate and modify the knowledge base and the decision rules in an automatic way. Furthermore, it is able to adapt the knowledge base to the slow changes produced by disturbing factors, such as humidity and temperature. On the other hand, because this system maintains a rule-based structure it is very easy to incorporate expert human knowledge.     

Fuzzy Dempster–Shafer reasoning for rule-based classifiers

In real classification problems intrinsically vague information often coexist with conditions of “lack of specificity” originating from evidence not strong enough to induce knowledge, but only degrees of belief or credibility regarding class assignments. The problem has been addressed here by proposing a fuzzy Dempster–Shafer model (FDS) for multisource classification purposes. The salient aspect of the work is the definition of an empirical learning strategy for the automatic generation of fuzzy Dempster–Shafer classification rules from a set of exemplified training data. Dempster–Shafer measures of uncertainty are semantically related to conditions of ambiguity among the data and then automatically set during the learning process. Partial reduced beliefs in class assignments are then induced and explicitly represented when generating classification rules. The fuzzy deductive apparatus has been modified and extended to integrate the Dempster–Shafer propagation of evidence. The strategy has been applied to a standard classification problem in order to develop a sensitivity analysis in an easily controlled domain. A second experimental test has been conducted in the field of natural risk assessment, where vagueness and lack of specificity conditions are prevalent. These empirical tests show that classification benefits from the combination of the fuzzy and Dempster–Shafer models especially when conditions of lack of specifity among data are prevalent. ©1999 John Wiley & Sons, Inc.