Fuzzy functions with support vector machines

A new fuzzy system modeling (FSM) approach that identifies the fuzzy functions using support vector machines (SVM) is proposed. This new approach is structurally different from the fuzzy rule base approaches and fuzzy regression methods. It is a new alternate version of the earlier FSM with fuzzy functions approaches. SVM is applied to determine the support vectors for each fuzzy cluster obtained by fuzzy c-means (FCM) clustering algorithm. Original input variables, the membership values obtained from the FCM together with their transformations form a new augmented set of input variables. The performance of the proposed system modeling approach is compared to previous fuzzy functions approaches, standard SVM, LSE methods using an artificial sparse dataset and a real-life non-sparse dataset. The results indicate that the proposed fuzzy functions with support vector machines approach is a feasible and stable method for regression problems and results in higher performances than the classical statistical methods.     

Fuzzy functions based ARX model and new fuzzy basis function models for nonlinear system identification

In this study, auto regressive with exogenous input (ARX) modeling is improved with fuzzy functions concept (FF-ARX). Fuzzy function with least squares estimation (FF-LSE) method has been recently developed and widely used with a small improvement with respect to least squares estimation method (LSE). FF-LSE is structured with only inputs and their membership values. This proposed model aims to increase the capability of the FF-LSE by widening the regression matrix with lagged input–output values. In addition, by using same idea, we proposed also two new fuzzy basis function models. In the first, basis of the fuzzy system and lagged input–output values are structured together in the regression matrix and named as “L-FBF”. Secondly, instead of using basis function, the membership values of the lagged input–output values are used in the regression matrix by using Gaussian membership functions, called “M-FBF”. Therefore, the power of the fuzzy basis function is also enhanced. For the corresponding models, antecedent part parameters for the input vectors are determined with fuzzy c-means (FCM) clustering algorithm. The consequent parameters of the all models are estimated with the LSE. The proposed models are utilized and compared for the identification of nonlinear benchmark problems.     

基于模糊神经网络方法实现茶味信号识别的研究

提出一种基于模糊c-均值聚类(FCM)的模糊神经网络模型用于荼味信号识剐的方法。该方法采用模糊c-均值聚类实现模糊神经网络中模糊子集及其隶属度函教的自动确定，并对模糊加权型推理法进行了改进，在此基础上构枣了一个模糊神经网络模型。通过5种茶味信号识别的仿真实验，表明本文提出方法的有效性。     

Development of a systematic methodology of fuzzy logic modeling

This paper proposes a systematic methodology of fuzzy logic modeling for complex system modeling. It has a unified parameterized reasoning formulation, an improved fuzzy clustering algorithm, and an efficient strategy of selecting significant system inputs and their membership functions. The reasoning mechanism introduces 4 parameters whose variation provides a continuous range of inference operation. As a result, we are no longer restricted to standard extremes in any step of reasoning. The fuzzy model itself can then adjust the reasoning process by optimizing the inference parameters based on input-output data. The fuzzy rules are generated through fuzzy c-means (FCM) clustering. Major bottlenecks are addressed and analytical solutions are suggested. We also address the classification process to extend the derived fuzzy partition to the entire output space. In order to select suitable input variables among a finite number of candidates (unlike traditional approaches) we suggest a new strategy through which dominant input parameters are assigned in one step and no iteration process is required. Furthermore, a clustering technique called fuzzy fine clustering is introduced to assign the input membership functions. In order to evaluate the proposed methodology, two examples-a nonlinear function and a gas furnace dynamic procedure-are investigated in detail. The significant improvement of the model is concluded compared to other fuzzy modeling approaches     

Constraint-Based Fuzzy Models for an Environment with Heterogeneous Information-Granules

A novel framework for fuzzy modeling and model-based control design is described. Based on the theory of fuzzy constraint processing, the fuzzy model can be viewed as a generalized Takagi-Sugeno （TS） fuzzy model with fuzzy functional consequences. It uses multivariate antecedent membership functions obtained by granular-prototype fuzzy clustering methods and consequent fuzzy equations obtained by fuzzy regression techniques. Constrained optimization is used to estimate the consequent parameters, where the constraints are based on control-relevant a priori knowledge about the modeled process. The fuzzy-constraint-based approach provides the following features. 1） The knowledge base of a constraint-based fuzzy model can incorporate information with various types of fuzzy predicates. Consequently, it is easy to provide a fusion of different types of knowledge. The knowledge can be from data-driven approaches and/or from controlrelevant physical models. 2） A corresponding inference mechanism for the proposed model can deal with heterogeneous information granules. 3） Both numerical and linguistic inputs can be accepted for predicting new outputs. The proposed techniques are demonstrated by means of two examples： a nonlinear function-fitting problem and the well-known Box-Jenkins gas furnace process. The first example shows that the proposed model uses fewer fuzzy predicates achieving similar results with the traditional rule-based approach, while the second shows the performance can be significantly improved when the control-relevant constraints are considered.     

A structure identification method of submodels for hierarchical fuzzy modeling using the multiple objective genetic algorithm

Fuzzy models describe nonlinear input‐output relationships with linguistic fuzzy rules. A hierarchical fuzzy modeling is promising for identification of fuzzy models of target systems that have many input variables. In the identification, (1) determination of a hierarchical structure of submodels, (2) selection of input variables of each submodel, (3) division of input and output space, (4) tuning of membership functions, and (5) determination of fuzzy inference method are carried out. This article presents a hierarchical fuzzy modeling method with an uneven division method of input space of each submodel. For selecting input variables of submodels, the multiple objective genetic algorithm (MOGA) is utilized. MOGA finds multiple models with different input variables and different numbers of fuzzy rules as compromising solutions. A human designer can choose desirable ones from these candidates. The proposed method is applied to acquisition of fuzzy rules from cyclists' pedaling data. In spite of a small number of data, the obtained model was able to give detailed suggestions to each cyclist. © 2002 Wiley Periodicals, Inc.     

基于混合聚类算法的模糊函数系统辨识方法

针对传统模糊系统存在的结构难以确定和参数辨识复杂的问题,提出了一种基于混合聚类算法的模糊函数系统辨识算法.与一般的模糊函数系统相比,混合聚类算法结合模糊C均值和模糊C回归模型聚类算法的样本距离.在模型预测部分,采用高斯函数计算每个输入变量的隶属度,利用输入变量隶属度的模糊化算子得到输入向量的隶属度.应用于Box-Jenkins煤气炉数据、一个双入单出的非线性系统和Mackey-Glass混沌时间序列数据的试验结果表明,本文算法具有很好的辨识效果,从而验证了本文算法的有效性与实用性.     

有混合数据输入的自适应模糊神经推理系统

现有数据建模方法大多依赖于定量的数值信息,而对于数值与分类混合输入的数据建模问题往往根据分类变量组合建立多个子模型,当有多个分类变量输入时易出现子模型数据分布不均匀、训练耗时长等问题.针对上述问题,提出一种具有混合数据输入的自适应模糊神经推理系统模型,在自适应模糊推理系统的基础上,引入激励强度转移矩阵和结论影响矩阵,采用基于高氏距离的减法聚类辨识模型结构,通过混合学习算法训练模型参数,使数值与分类混合数据对模糊规则的前后件参数同时产生作用,共同影响模型输出.仿真实验分析了分类数据对模型规则后件的作用以及结构辨识算法对模糊规则数的影响,与其他几种混合数据建模方法对比表明本文所提出的模型具有较高的预测精度和计算效率.     

一种基于聚类的超闭球模糊神经网络

针对一类不确定非线性多输入多输出复杂系统,根据系统的输入输出数据对,提出一种基于聚类的超闭球模糊神经网络系统．该系统通过改进的模糊聚类方法（FCM）确定模糊规则数,采用高维隶属度函数取代常规的单维隶属度函数,并对隶属度函数中心值和隶属度函数参数采用一步通过算法,所提方法可降低系统的模糊规则数,简化网络计算．此外,当系统的输入输出发生变化时,可实现模糊规则库的在线修改．仿真实例验证了所提方法的有效性．     

Linear Fuzzy Clustering With Selection of Variables Using Graded Possibilistic Approach

Linear fuzzy clustering is a useful tool for knowledge discovery in databases (KDD), and several modifications have been proposed in order to analyze real world data. This paper proposes a new approach for estimating local linear models, in which linear fuzzy clustering is performed by selecting variables that are useful for extracting correlation structure in each cluster. The new clustering model uses two types of memberships. One is the conventional membership that represents the degree of membership of each sample in each cluster. The other is the additional parameter that represents the relative responsibility of each variable for estimation of local linear models. The additional membership takes large values when the variable has close relationship with local principal components, and is calculated by using the graded possibilistic approach. Numerical experiments demonstrate that the proposed method is useful for identifying local linear model taking typicality of each variable into account.     

Fuzzy functions with LSE

“Fuzzy Functions” are proposed to be determined by the least squares estimation (LSE) technique for the development of fuzzy system models. These functions, “Fuzzy Functions with LSE” are proposed as alternate representation and reasoning schemas to the fuzzy rule base approaches. These “Fuzzy Functions” can be more easily obtained and implemented by those who are not familiar with an in-depth knowledge of fuzzy theory. Working knowledge of a fuzzy clustering algorithm such as FCM or its variations would be sufficient to obtain membership values of input vectors. The membership values together with scalar input variables are then used by the LSE technique to determine “Fuzzy Functions” for each cluster identified by FCM. These functions are different from “Fuzzy Rule Base” approaches as well as “Fuzzy Regression” approaches. Various transformations of the membership values are included as new variables in addition to original selected scalar input variables; and at times, a logistic transformation of non-scalar original selected input variables may also be included as a new variable. A comparison of “Fuzzy Functions-LSE” with Ordinary Least Squares Estimation (OLSE)” approach show that “Fuzzy Function-LSE” provide better results in the order of 10% or better with respect to RMSE measure for both training and test cases of data sets.     

A Highly Accurate Model-Free Motion Control System with a Mamdani Fuzzy Feedback Controller combined with a TSK Fuzzy Feed-forward Controller

In this paper, a new intelligent robot motion control architecture – a highly accurate model-free fuzzy motion control- is proposed in order to achieve improved robot motion accuracy and dynamic performance. Its architecture combines a Mamdani fuzzy proportional (P) and a conventional integral (I) plus derivative (D) controller for the feedback part of the system, and a Takagi-Sugeno-Kang fuzzy controller for the feed-forward, nonlinear part. The fuzzy P + ID controller improves the performance of the nonlinear system, and the TSK fuzzy controller uses a TSK fuzzy inference system based on extended subtractive- clustering method which integrates information on joint angular displacement, velocity and acceleration for torque identification. The advantage of this kind of model-free control is that it uses the information directly from the input/output of the nonlinear system, without any complex robot model computation, in order to decrease the control system’s sensitivity to any dynamical uncertainty. Furthermore, parametric search for clustering parameters in extended subtractive clustering secures the high accuracy of the system identification. Consequently, this proposed model-free fuzzy motion control benefits from the advantages of two kinds of fuzzy system. It not only incorporates flexible design, good performance and simple conception but also ensures precise motion control and great robustness. Comparisons with other intelligent models and results from numerical studies on a 4-bar planar parallel mechanism show the effectiveness and competitiveness of the proposed control.     

基于改进遗传算法的非线性系统模糊辨识新方法

提出一种基于改进遗传算法和递推最小二乘的非线性模糊辨识新算法.该辨识方法包含结构辨识辨出和参数辨识,结构辨识即输入空间的模糊划分,采用具有自适应性的广义高斯隶属函数;参数辨识包含前提参数和结论参数,用基于动态比例变换的改进遗传算法优化高斯函数的前提参数,用递推最小二乘辨识模糊模型的结论参数.最后通过著名的Box-Jenkins煤气炉数据仿真(仿真环境:MATLAB 6.5,计算机主频2.4 GHz,内存512 MB),并根据输入变量个数和模糊规则数,得到均方误差以证明本文方法的辨识精度,将该文辨识方法与其他方法进行比较,验证了该方法辨识精度更高.     

基于模糊聚类的非线性系统模糊辨识算法

针对模糊聚类算法中数据和运算耗时很长,不适于在线建模与控制的问题,基于模糊聚类型隶属函数和EUM方法,提出了一种新的模糊辨识算法。该方法省去了求解聚类中心的迭代过程,计算时间显著减少。采用该方法对Box—Jenkins煤气炉数据和Mackey—Glass混沌时间序列进行了仿真,结果证明了该方法的有效性。     

Hybrid identification of fuzzy rule‐based models

In this study, we propose a hybrid identification algorithm for a class of fuzzy rule‐based systems. The rule‐based fuzzy modeling concerns structure optimization and parameter identification using the fuzzy inference methods and hybrid structure combined with two methods of optimization theories for nonlinear systems. Two types of inference methods of a fuzzy model concern a simplified and linear type of inference. The proposed hybrid optimal identification algorithm is carried out using a combination of genetic algorithms and an improved complex method. The genetic algorithms determine initial parameters of the membership function of the premise part of the fuzzy rules. In the sequel, the improved complex method (being in essence a powerful auto‐tuning algorithm) leads to fine‐tuning of the parameters of the respective membership functions. An aggregate performance index with a weighting factor is proposed in order to achieve a balance between performance of the fuzzy model obtained for the training and testing data. Numerical examples are included to evaluate the performance of the proposed model. They are also contrasted with the performance of the fuzzy models existing in the literature. © 2002 John Wiley & Sons, Inc.     

基于鲁棒加权模糊聚类的污水处理过程监测方法

针对非线性强、先验故障知识少、异常工况识别难的污水处理过程监测问题,提出一种基于鲁棒加权模糊c均值(Robust weighted fuzzy c-means, RoW-FCM)聚类与核偏最小二乘(Kernel partial least squares, KPLS)的过程监测方法.首先,针对污水处理过程的高维非线性耦合特性,采用核偏最小二乘对高维输入变量进行降维;其次,针对传统基于最近邻分配的模糊c均值算法对离群点敏感以及存在聚类不平衡簇的问题,提出充分考虑样本间相互关系的基于鲁棒加权模糊c均值聚类算法.通过引入可能性划分矩阵作为权值参数实现不同样本数据的区分加权,提高了离群点数据聚类的鲁棒性,同时引入聚类大小控制参数解决不平衡簇的问题.进一步将基于鲁棒加权模糊c均值算法对核偏最小二乘降维后的得分矩阵进行聚类,利用聚类得到的隶属度矩阵实现异常工况的检测;最后,建立隶属度矩阵与过程变量的回归模型,并利用得到的变量贡献矩阵描述变量对各个簇的解释程度,实现异常工况的识别.数值仿真以及污水处理过程数据实验表明该方法具有更好的鲁棒性能,在异常工况检测和识别上具有较好的效果.     

基于模糊关联规则挖掘的模糊入侵检测

论文把模糊关联规则挖掘算法引入到网络的入侵检测,利用该算法从网络数据集中提取出具有较高可信性和完备性的模糊规则,并利用这些规则设计和实现用于入侵检测的模糊分类器。同时,针对模糊关联规则挖掘算法,利用K-means聚类算法建立属性的模糊集和模糊隶属函数,并提出了一种双置信度算法以增加模糊规则的有效性和完备性。最后,给出了详实的实验过程和结果,以此来验证提出的模糊入侵检测方法的有效性。     

一种新型的基于遗传算法的进化模糊推理系统

介绍了遗传算法和进化模糊推理系统的融合方式及结构,应用一种新型的基于遗传算法的进化模糊推理系统动态自适应的在线学习和离线学习。使用进化聚类方法,模糊规则在系统执行过程中进行创建和更新,并且采用遗传算法优化进化聚类的结果,修改成员的隶属度函数,通过模糊推理系统计算系统的输出。     

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。     

Evolving Compact and Interpretable Takagi–Sugeno Fuzzy Models With a New Encoding Scheme

Developing Takagi–Sugeno fuzzy models by evolutionary algorithms mainly requires three factors: an encoding scheme, an evaluation method, and appropriate evolutionary operations. At the same time, these three factors should be designed so that they can consider three important aspects of fuzzy modeling: modeling accuracy, compactness, and interpretability. This paper proposes a new evolutionary algorithm that fulfills such requirements and solves fuzzy modeling problems. Two major ideas proposed in this paper lie in a new encoding scheme and a new fitness function, respectively. The proposed encoding scheme consists of three chromosomes, one of which uses unique chained possibilistic representation of rule structure. The proposed encoding scheme can achieve simultaneous optimization of parameters of antecedent membership functions and rule structures with the new fitness function developed in this paper. The proposed fitness function consists of five functions that consider three evaluation criteria in fuzzy modeling problems. The proposed fitness function guides evolutionary search direction so that the proposed algorithm can find more accurate compact fuzzy models with interpretable antecedent membership functions. Several evolutionary operators that are appropriate for the proposed encoding scheme are carefully designed. Simulation results on three modeling problems show that the proposed encoding scheme and the proposed fitness functions are effective in finding accurate, compact, and interpretable Takagi–Sugeno fuzzy models. From the simulation results, it is shown that the proposed algorithm can successfully find fuzzy models that approximate the given unknown function accurately with a compact number of fuzzy rules and membership functions. At the same time, the fuzzy models use interpretable antecedent membership functions, which are helpful in understanding the underlying behavior of the obtained fuzzy models.