Crossover enhancements in GEFREX

This letter describes some improvements to the crossover operator in the genetic-neuro-fuzzy algorithm called genetic fuzzy rule extractor (GEFREX). Although, the new crossovers studied are very simple, the performance of GEFREX, in terms of learning time, is decidedly improved.     

Induction of descriptive fuzzy classifiers with the Logitboost algorithm

Recently, Adaboost has been compared to greedy backfitting of extended additive models in logistic regression problems, or “Logitboost". The Adaboost algorithm has been applied to learn fuzzy rules in classification problems, and other backfitting algorithms to learn fuzzy rules in modeling problems but, up to our knowledge, there are not previous works that extend the Logitboost algorithm to learn fuzzy rules in classification problems.In this work, Logitboost is applied to learn fuzzy rules in classification problems, and its results are compared with that of Adaboost and other fuzzy rule learning algorithms. Contradicting the expected results, it is shown that the basic extension of the backfitting algorithm to learn classification rules may produce worse results than Adaboost does. We suggest that this is caused by the stricter requirements that Logitboost demands to the weak learners, which are not fulfilled by fuzzy rules. Finally, it is proposed a prefitting based modification of the Logitboost algorithm that avoids this problem     

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.     

Efficient Self-Evolving Evolutionary Learning for Neurofuzzy Inference Systems

This study proposes an efficient self-evolving evolutionary learning algorithm (SEELA) for neurofuzzy inference systems (NFISs). The major feature of the proposed SEELA is that it is based on evolutionary algorithms that can determine the number of fuzzy rules and adjust the NFIS parameters. The SEELA consists of structure learning and parameter learning. The structure learning attempts to determine the number of fuzzy rules. A subgroup symbiotic evolution is adopted to yield several variable fuzzy systems, and an elite-based structure strategy is adopted to find a suitable number of fuzzy rules for solving a problem. The parameter learning is to adjust parameters of the NFIS. It is a hybrid evolutionary algorithm of cooperative particle swarm optimization (CPSO) and cultural algorithm, called cultural CPSO (CCPSO). The CCPSO, which uses cooperative behavior among multiple swarms, can increase the global search capacity using the belief space. Experimental results demonstrate that the proposed method performs well in predicting time series and solving nonlinear control problems.      

GENERATING FUZZY RULES FROM TRAINING DATA CONTAINING NOISE FOR HANDLING CLASSIFICATION PROBLEMS

It is obvious that one of the important tasks in a fuzzy system is to find a set of rules to deal with a specific classification problem. In recent years, many researchers focused on the research topic of generating fuzzy rules from training data for handling classification problems. In a previous paper, we presented an algorithm to construct membership functions and to generate fuzzy rules from training examples. In this paper, we extend that work to propose a new algorithm to generate fuzzy rules from training data containing noise to deal with classification problems. The proposed algorithm gets a higher classification accuracy rate and generates fewer fuzzy rules and fewer input attributes in the antecedent portions of the generated fuzzy rules.     

Fuzzy wavelet neural network based on fuzzy clustering and gradient techniques for time series prediction

This paper presents the development of fuzzy wavelet neural network system for time series prediction that combines the advantages of fuzzy systems and wavelet neural network. The structure of fuzzy wavelet neural network (FWNN) is proposed, and its learning algorithm is derived. The proposed network is constructed on the base of a set of TSK fuzzy rules that includes a wavelet function in the consequent part of each rule. A fuzzy c-means clustering algorithm is implemented to generate the rules, that is the structure of FWNN prediction model, automatically, and the gradient-learning algorithm is used for parameter identification. The use of fuzzy c-means clustering algorithm with the gradient algorithm allows to improve convergence of learning algorithm. FWNN is used for modeling and prediction of complex time series and prediction of foreign-exchange rates. Exchange rates are dynamic process that changes every day and have high-order nonlinearity. The statistical data for the last 2 years are used for the development of FWNN prediction model. Effectiveness of the proposed system is evaluated with the results obtained from the simulation of FWNN-based systems and with the comparative simulation results of previous related models.     

Genetic reinforcement learning through symbiotic evolution forfuzzy controller design

An efficient genetic reinforcement learning algorithm for designing fuzzy controllers is proposed in this paper. The genetic algorithm (GA) adopted in this paper is based upon symbiotic evolution which, when applied to fuzzy controller design, complements the local mapping property of a fuzzy rule. Using this Symbiotic-Evolution-based Fuzzy Controller (SEFC) design method, the number of control trials, as well as consumed CPU time, are considerably reduced when compared to traditional GA-based fuzzy controller design methods and other types of genetic reinforcement learning schemes. Moreover, unlike traditional fuzzy controllers, which partition the input space into a grid, SEFC partitions the input space in a flexible way, thus creating fewer fuzzy rules. In SEFC, different types of fuzzy rules whose consequent parts are singletons, fuzzy sets, or linear equations (TSK-type fuzzy rules) are allowed. Further, the free parameters (e.g., centers and widths of membership functions) and fuzzy rules are all tuned automatically. For the TSK-type fuzzy rule especially, which put the proposed learning algorithm in use, only the significant input variables are selected to participate in the consequent of a rule. The proposed SEFC design method has been applied to different simulated control problems, including the cart-pole balancing system, a magnetic levitation system, and a water bath temperature control system. The proposed SEFC has been verified to be efficient and superior from these control problems, and from comparisons with some traditional GA-based fuzzy systems.     

Neural networks that learn from fuzzy if-then rules

An architecture for neural networks that can handle fuzzy input vectors is proposed, and learning algorithms that utilize fuzzy if-then rules as well as numerical data in neural network learning for classification problems and for fuzzy control problems are derived. The learning algorithms can be viewed as an extension of the backpropagation algorithm to the case of fuzzy input vectors and fuzzy target outputs. Using the proposed methods, linguistic knowledge from human experts represented by fuzzy if-then rules and numerical data from measuring instruments can be integrated into a single information processing system (classification system or fuzzy control system). It is shown that the scheme works well for simple examples     

A new Neuro-Fuzzy Inference System with Dynamic Neurons (NFIS-DN) for system identification and time series forecasting

A new Neuro-Fuzzy Inference System with Dynamic Neurons or NFIS-DN is presented here for discrete time dynamic system identification and time series forecasting problems. The proposed dynamic system based neuron, referred to as Dynamic Neuron (DN) is realized by a discrete-time nonlinear state-space model. The DN is designed such way, that the output considers only the effect of finite past instances, enabling the system with finite memory. The NFIS-DN model has five layers, and DNs are employed only in the layers handling crisp values. The antecedent and the consequent parameters of NFIS-DN are updated using a self-regulated backpropagation through time learning algorithm. The performance evaluation of NFIS-DN has been carried-out using benchmark problems in the areas of nonlinear system identification and time series forecasting. The results are compared with the state-of-the-art method on the neural fuzzy networks. The obtained results clearly suggest that the NFIS-DN performs significantly better while using a smaller or similar number of fuzzy rules. Finally the practical application of the NFIS-DN has been demonstrated using two real-world problems.     

Mining fuzzy specific rare itemsets for education data

Association rule mining is an important data analysis method for the discovery of associations within data. There have been many studies focused on finding fuzzy association rules from transaction databases. Unfortunately, in the real world, one may have available relatively infrequent data, as well as frequent data. From infrequent data, we can find a set of rare itemsets that will be useful for teachers to find out which students need extra help in learning. While the previous association rules discovery techniques are able to discover some rules based on frequency, this is insufficient to determine the importance of a rule composed of frequency-based data items. To remedy this problem, we develop a new algorithm based on the Apriori approach to mine fuzzy specific rare itemsets from quantitative data. Finally, fuzzy association rules can be generated from these fuzzy specific rare itemsets. The patterns are useful to discover learning problems. Experimental results show that the proposed approach is able to discover interesting and valuable patterns from the survey data.     

一种模糊推理过程神经网络及其应用研究

针对带有过程性模糊信息或动态领域规则的时变信息处理问题,提出一种模糊推理过程神经网络.该模型将模糊过程推理规则与数值型过程神经网络的动态信息处理机制相结合,将推理规则表示为过程神经元.利用过程神经网络的学习性质来实现对过程性定量与定性混合信息的自适应处理.分析了模糊推理过程神经网络的信息处理机制,并给出了相应的学习算法.以抽油机平衡诊断为例,实验结果验证了所提出模型和算法的有效性.     

A recurrent fuzzy-neural model for dynamic system identification

This paper presents a fuzzy modeling approach for identification of dynamic systems. In particular, a new fuzzy model, the Dynamic Fuzzy Neural Network (DFNN), consisting of recurrent TSK rules, is developed. The premise and defuzzification parts are static while the consequent parts of the fuzzy rules are recurrent neural networks with internal feedback and time delay synapses. The network is trained by means of a novel learning algorithm, named Dynamic-Fuzzy Neural Constrained Optimization Method (D-FUNCOM), based on the concept of constrained optimization. The proposed algorithm is general since it can be applied to locally as well as fully recurrent networks, regardless of their structures. An adaptation mechanism of the maximum parameter change is presented as well. The proposed dynamic model, equipped with the learning algorithm, is applied to several temporal problems, including modeling of a NARMA process and the noise cancellation problem. Performance comparisons are conducted with a series of static and dynamic systems and some existing recurrent fuzzy models. Simulation results show that DFNN compares favorably with its competing rivals and thus it can be considered for efficient system identification.     

Incremental fuzzy temporal association rule mining using fuzzy grid table

Traditional temporal association rules mining algorithms cannot dynamically update the temporal association rules within the valid time interval with increasing data. In this paper, a new algorithm called incremental fuzzy temporal association rule mining using fuzzy grid table (IFTARMFGT) is proposed by combining the advantages of boolean matrix with incremental mining. First, multivariate time series data are transformed into discrete fuzzy values that contain the time intervals and fuzzy membership. Second, in order to improve the mining efficiency, the concept of boolean matrices was introduced into the fuzzy membership to generate a fuzzy grid table to mine the frequent itemsets. Finally, in view of the Fast UPdate (FUP) algorithm, fuzzy temporal association rules are incrementally mined and updated without repeatedly scanning the original database by considering the lifespan of each item and inheriting the information from previous mining results. The experiments show that our algorithm provides better efficiency and interpretability in mining temporal association rules than other algorithms.

     

A neural fuzzy system with fuzzy supervised learning

A neural fuzzy system learning with fuzzy training data (fuzzy if-then rules) is proposed in this paper. This system is able to process and learn numerical information as well as linguistic information. At first, we propose a five-layered neural network for the connectionist realization of a fuzzy inference system. The connectionist structure can house fuzzy logic rules and membership functions for fuzzy inference. We use alpha-level sets of fuzzy numbers to represent linguistic information. The inputs, outputs, and weights of the proposed network can be fuzzy numbers of any shape. Furthermore, they can be hybrid of fuzzy numbers and numerical numbers through the use of fuzzy singletons. Based on interval arithmetics, a fuzzy supervised learning algorithm is developed for the proposed system. It extends the normal supervised learning techniques to the learning problems where only linguistic teaching signals are available. The fuzzy supervised learning scheme can train the proposed system with desired fuzzy input-output pairs which are fuzzy numbers instead of the normal numerical values. With fuzzy supervised learning, the proposed system can be used for rule base concentration to reduce the number of rules in a fuzzy rule base. Simulation results are presented to illustrate the performance and applicability of the proposed system.     

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.     

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.     

在FCS环境中神经网络模糊控制的研究

本文提出了在ＦＣＳ环境中的一种模糊控制方法，该方法采用了模糊ＩＦ．ＴＨＥＮ规则和数字数据两种方法进行学习在ＦＣＳ环境中，系统的正确性不但依赖于其计算出的逻辑结果，而且还依赖于该结果的计算时间。针对上述特征，提出了一种能够控制模糊输入矢量的神经网络体系结构，它将一个模糊输入矢量映射到其模糊输出中。     

模糊规则的学习及其在非线性系统建模中的应用

探讨用神经网络的学习算法及模糊推理方法为非线性系统建模的问题.给出了学习模糊规则的新算法.这个算法首先用竞争学习为训练样本的输入空间进行聚类,然后为其确定区域划分边界,并按样本输入区域学习模糊规则.文中对于模糊规则提出了相应的模糊推理算法.并用算例验证了本文算法的有效性.     

A systematic approach to a self-generating fuzzy rule-table forfunction approximation

In this paper, a systematic design is proposed to determine fuzzy system structure and learning its parameters, from a set of given training examples. In particular, two fundamental problems concerning fuzzy system modeling are addressed: 1) fuzzy rule parameter optimization and 2) the identification of system structure (i.e., the number of membership functions and fuzzy rules). A four-step approach to build a fuzzy system automatically is presented: Step 1 directly obtains the optimum fuzzy rules for a given membership function configuration. Step 2 optimizes the allocation of the membership functions and the conclusion of the rules, in order to achieve a better approximation. Step 3 determines a new and more suitable topology with the information derived from the approximation error distribution; it decides which variables should increase the number of membership functions. Finally, Step 4 determines which structure should be selected to approximate the function, from the possible configurations provided by the algorithm in the three previous steps. The results of applying this method to the problem of function approximation are presented and then compared with other methodologies proposed in the bibliography.     

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.