Fuzzy inference systems with no any base and linearly parameter growth

A class of new fuzzy inference systems New-FISs is presented. Compared with the standard fuzzy system,New-FIS is still a universal approximator and has no fuzzy rule base and linearly parameter growth. Thus, it effectively overcomes the second "curse of dimensionality": there is an exponential growth in the number of parameters of a fuzzy system as the number of input variables, resulting in surprisingly reduced computational complexity and being especially suitable for applications, where the complexity is of the first importance with respect to the approximation accuracy.     

基于遗传算法的广义Takagi-Sugeno模糊逻辑系统最优参数辨识

针对Takagi-Sugeno模糊逻辑系统的隶属函数不具有自适应性且模糊规则数的确定 带有很大的人为主观性,这里引入了一类广义Takagi-Sugeno模糊逻辑系统;在模型实现上，以 广义Takagi-Sugeno模型为个体,采用简单、有效的矩阵编码方式,借助遗传算法得到一个次优 的广义Takagi-Sugeno模糊系统模型,该模型不仅能很好地逼近所要辨识的非线性系统,而且 还具有较低的复杂度.仿真结果表明了广义Takagi-Sugeno模型及其参数辨识方法的正确性和 有效性.     

Orthogonal Fuzzy Rule-Based Systems: Selection of Optimum Rules

In this paper, the concept of orthogonal fuzzy rule-based systems is introduced. Orthogonal rules are an extension to the definition of orthogonal vectors when the vectors are vectors of membership functions in the antecedent part of rules. The number and combination of rules in a fuzzy rule-based system will be optimised by applying orthogonal rules. The number of rules, and subsequently the complexity of the fuzzy rule-based systems, are directly associated with the number of input variables and distinguishable membership functions for each individual input variable. A subset of rules can be used if it is known which subset provides closer behaviour to the case when all rules are used. Orthogonal fuzzy rule-based systems are proposed as a judgment as to whether the optimal rules are selected. The application of orthogonal fuzzy rules becomes essential when fuzzy rule-based systems containing many inputs are used. An illustrative example is presented to create a model for the solder paste printing stage of surface mount tech-nology.     

Avoiding exponential parameter growth in fuzzy systems

For standard fuzzy systems where the input membership functions are defined on a grid on the input space, and all possible combinations of rules are used, there is an exponential growth in the number of parameters of the fuzzy system as the number of input dimensions increases. This “curse of dimensionality” effect leads to problems with design of fuzzy controllers (e.g., how to tune all these parameters), training of fuzzy estimators (e.g., complexity of a gradient algorithm for training, and problems with “over parameterization” that lead to poor convergence properties), and with computational complexity in the implementation for practical problems. We introduce a fuzzy system whose number of parameters grows linearly depending upon the number of inputs, even though it is constructed by using all possible combinations of the membership functions in defining the rules. We prove that this fuzzy system is equivalent to the standard fuzzy system as long as its parameters are specified in a certain way. Then, we show that it still holds the universal approximator property by using the Stone-Welerstrass theorem. Finally, we illustrate the performance of the fuzzy system via an application     

MATLAB在模糊控制系统仿真中的应用

模糊控制系统的设计是模糊控制系统应用的重要问题之一,而系统的仿真是设计中的重要步骤和必要的保证,本文首先简要介绍了MATLAB语言、模糊逻辑工具箱和SIMULINK工具箱,然后着重介绍如何利用模糊逻辑工具箱、SIMULINK工具箱进行模糊控制系统的仿真,并给出具体实例,这种方法克服了传统用C语言进行仿真的复杂,不方便的缺点,使模糊控制系统的仿真变得容易、直观且迅速。     

设计模糊控制器的一种方法

本文提出一种设计模糊控制器（ＦＣ）的方法,该方法将于Ｅｉ,ＥＣｊ,Ｕｋ分别定义为各自论域上的模糊划分,采用代数乘和代数加运算,量化等级可以根据需要而定,简化算法可以实现实时在线计算,内存只存储控制规则和隶属度函数,计算复杂度与量化等级无关;设计的模糊控制器具有良好的动态和稳态性能。     

Fuzzy normal regression model and related neural networks

A fuzzy normal regression model that takes normal fuzzy numbers as its elements for fuzzy sampling points is presented in this paper. This is a continuation of the authors work in the paper [1]. The related fuzzy regression NN system makes the model more flexible in order to accommodate the renewing or refining of the sampling process. The essential ideas of fuzzy regression model and the related neural networks will be explained in a clear manner in this work using an application problem.     

Fuzzy neural networks for estimation and fuzzy controller design: simulation study for a pulp batch digester

A structural implementation of a fuzzy inference system through connectionist network based on MLP with logical neurons connected through binary and numerical weights is considered. The resulting fuzzy neural network is trained using classical backpropagation to learn the rules of inference of a fuzzy system, by adjustment of the numerical weights. For controller design, training is carried out off line in a closed loop simulation. Rules for the fuzzy logic controller are extracted from the network by interpreting the consequence weights as measure of confidence of the underlying rule. The framework is used in a simulation study for estimation and control of a pulp batch digester. The controlled variable, the Kappa number, a measure of lignin content in the pulp, which is not measurable is estimated through temperature and liquor concentration using the fuzzy neural network. On the other hand a fuzzy neural network is trained to control the Kappa number and rules are extracted from the trained network to construct a fuzzy logic controller.     

关于模糊PID控制器推理机维数的研究

对一维(1D)至三维(3D)模糊PID控制器进行了系统的分析研究,提出了四项系 统功能特性指标来评价不同结构的控制器;这包括控制分量合成,耦合影响,增益相关和规则 增长.通过对最常见的二维Mamdani模糊控制器进行分析研究,发现该控制器存在功能缺 陷.为此,提出了最优结构的一维模糊PID控制器.该控制器采用了"1D-3D"映射关系的模糊 推理机,从而实现了三个控制分量可以独立不相关的调整功能.通过与二维和三维控制器比 较结果表明,一维控制器具有最佳系统功能特性.     

污水处理实验系统中溶解氧模糊控制器的设计

本文在分析了污水处理的生物氧化过程中溶解氧（DO）控制的重要性及复杂性后，提出用模糊控制的方法控制污水处理中的溶解氧，并设计了溶解氧模糊控制系统，为污水处理的自动控制提供了一个新的设计方法。     

变电站智能告警专家系统的不确定性知识表示

在变电站智能告警专家系统中,针对业务知识的不确定性和复杂性,文中设计了一种不确定性知识的表示方法,可以使采用该方法构建的知识库更有利于推理机的推理和知识库的自学习。该方法根据领域知识将变电站信号进行分层分类,以子知识库的形式进行知识的组织,克服了知识的复杂性。而且它采用一种模糊产生式表示业务知识,将模糊推理规则映射为模糊产生式,解决了知识的不确定性问题。实验分析表明,该方法适合进行变电站关联信号的告警推理,结合系统对知识的自学习机制,可以有效降低告警的差错率和虚警率。     

模糊理论在评价项目不确定性中的应用

项目活动的复杂性和动态性决定了项目的不确定性，概率及概率分布的观点比较适合于处理存在相关历史数据的项目的不确定性。面对很少有或根本没有可供参考的历史数据的项目，使用模糊方法处理不确定性是恰当的。文章使用模糊数来描述项目及活动的不确定性，并举出了一个具体算例。     

Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP

The lack of consistency in decision making can lead to inconsistent conclusions. In fuzzy analytic hierarchy process (fuzzy AHP) method, it is difficult to ensure a consistent pairwise comparison. Furthermore, establishing a pairwise comparison matrix requires judgments for a level with n criteria (alternatives). The number of comparisons increases as the number of criteria increases. Therefore, the decision makers judgments will most likely be inconsistent. To alleviate inconsistencies, this study applies fuzzy linguistic preference relations (Fuzzy LinPreRa) to construct a pairwise comparison matrix with additive reciprocal property and consistency. In this study, the fuzzy AHP method is reviewed, and then the Fuzzy LinPreRa method is proposed. Finally, the presented method is applied to the example addressed by Kahraman et al. [C. Kahraman, D. Ruan, I. Do?an, Fuzzy group decision making for facility location selection, Information Sciences 157 (2003) 135-153]. This study reveals that the proposed method yields consistent decision rankings from only n − 1 pairwise comparisons, which is the same result as in Kahraman et al. research. The presented fuzzy linguistic preference relations method is an easy and practical way to provide a mechanism for improving consistency in fuzzy AHP method.     

基于PLC的模糊控制污水处理系统

针对现代污水处理系统的复杂性和难以建立准确数学模型的特点,提出了一种用PLC对系统进行模糊控制的方法及实现。结果表明,基于该方法的系统抗干扰能力强,实现简单,取得了良好的调节品质。     

一种基于改进T-S模糊推理的模糊神经网络学习算法

针对模糊神经网络学习算法计算量过大,在预测模型设计中提出了基于改进T-S模糊推理的模糊神经网络学习算法。主要工作如下:首先,改进T-S模糊推理方法,定义基于偏移率的T-s模糊推理方法;然后,通过将此模糊推理方法与基于合成规则的模糊推理方法及距离型模糊推理方法相比较可以看出,所提方法有较少的计算量,且比较有效;最后,在此基础上改善了模糊神经网络学习算法,并将其应用于天气预测与安全态势预测。测试结果表明,该方法明显改善了学习效率,减少了预测模型设计中的学习次数与时间复杂度,并降低了学习误差。     

A NEW DESIGN APPROACH FOR FUZZY‐LEARNING FUZZY CONTROLLERS

In this paper, a new approach to designing fuzzy‐learning fuzzy controllers for a system plant without an exact mathematical model is presented. The cost function is defined as the square of the sliding function to alleviate the difficulty of overshoot when on‐line learning is conducted. The learning mechanism of a fuzzy controller is constructed so as to minimize the cost function with a set of linguistic rules. Moreover, to reduce the complexity of the fuzzy‐learning fuzzy controller, the fuzzy mechanism used for learning and the fuzzy mechanism contained in the fuzzy controller are designed so as to have the identical structures. Finally, simulations are included to show the effectiveness of the fuzzy‐learning fuzzy controllers.     

Web software fault prediction under fuzzy environment using MODULO-M multivariate overlapping fuzzy clustering algorithm and newly proposed revised prediction algorithm

In recent years some research works have been carried out on web software error analysis and reliability predictions. In all these works the web environment has been considered as crisp one, which is not a very realistic assumption. Moreover, web error forecasting remains unworthy for the researchers for quite a long time. Furthermore, among various well known forecasting techniques, fuzzy time series based methods are extensively used, though they are suffering from some serious drawbacks, viz., fixed sized intervals, using some fixed membership values (0, 0.5, and 1) and moreover, the defuzzification process only deals with the factor that is to be predicted. Prompted by these facts, the present authors have proposed a novel multivariate fuzzy forecasting algorithm that is able to remove all the aforementioned drawbacks as also can predict the future occurrences of different web failures (considering the web environment as fuzzy) with better predictive accuracy. Also, the complexity analysis of the proposed algorithm is done to unveil its better run time complexity. Moreover, the comparisons with the other existing frequently used forecasting algorithms were performed to demonstrate its better efficiency and predictive accuracy. Additionally, at the very end, the developed algorithm was applied on the real web failure data of http://www.ismdhanbad.ac.in/, the official website of ISM Dhanbad, India, collected from the corresponding HTTP log files.     

A self-organizing fuzzy control of weld pool size in GMA welding processes

In arc welding processes, because of the complexity and nonlinearity of heat transfer phenomena, it is often difficult to design an effective control system based upon an exact mathematical model. In this paper, a self-organizing fuzzy control method is proposed to obtain a uniform weld quality by regulation of the surface temperature at a desired level. The proposed control system is designed to comprise a combined structure of the fuzzy SOC with conventional PD control for improving the system's stability. The control experiments show that the proposed controller guarantees a uniform weld quality for various welding conditions.     

Fuzzy Conditional Probability Relations and their Applications in Fuzzy Information Systems

In our real-world applications, data may be imprecise in which levels or degrees of preciseness of data are intuitively different. In this case, fuzzy set expressions are considered as an alternative to represent the imprecise data. In general, the degree of similarity relationship between two fuzzy (imprecise) data in real-world applications may not necessarily be symmetric or transitive. In order to provide such a degree of similarity between two fuzzy data, we introduced the fuzzy conditional probability relation. The concept of a fuzzy conditional probability relation may be considered as a concrete example of weak similarity relation which in turn is a special type of fuzzy binary relation generalizing similarity relation. Two important applications concerning the application of Knowledge Discovery and Data Mining (KDD) in the presence of a fuzzy data table (usually called fuzzy information system), namely removing redundant objects and recognizing partial or total dependency of (domain) attributes, are considered induced by the fuzzy conditional probability relation. Here, the fuzzy information system contains precise as well as imprecise data (fuzzy values) about objects of interest characterized by some attributes. Related to the dependency of attributes, we introduce the fuzzy functional dependency that satisfies Armstrongs Axioms. In addition, we also discuss some interesting applications such as approximate data reduction and projection, approximate data querying and approximate joining in order to extend the query system.     

双层模糊系统融合中心约束型最小包含球

与传统的TSK模糊系统相比,改进的双层TSK模糊系统CTSK(Central TSK Fuzzy System)有如下优点:良好的可解释性、更好的鲁棒性、较强的逼近能力。但对于大样本或超大样本数据集,其时间复杂度和空间复杂度的开销都极大地限制了它的实用性。针对此不足,通过模糊系统融合中心约束型最小包含球(CCMEB)理论提出了CCMEB-CTSK(CCMEB-based CTSK)算法。该算法在继承CTSK优点的同时,又较好地实现了处理大样本和超大样本数据集的有效性和快速性。仿真实验研究分析了采用不同模糊规则数的CCMEB-CTSK的性能指标和运行时间的比较,以及训练样本不加噪声和加入噪声情况下CCMEB-CTSK泛化能力和鲁棒性能的测试。