Structural developments of fuzzy systems with the aid of information granulation

We introduce a design procedure for fuzzy systems using the concept of information granulation and genetic optimization. Information granulation and resulting information granules themselves become an important design aspect of fuzzy models. By accommodating the formalism of fuzzy sets, the model is geared towards capturing relationship between information granules (fuzzy sets) rather than concentrating on plain numeric data. Information granulation realized with the use of the standard C-Means clustering helps determine the initial values of the parameters of the fuzzy models. This in particular concerns such essential components of the rules as the initial apexes of the membership functions standing in the premise part of the fuzzy rules and the initial values of the polynomial functions standing in the consequence part. The initial parameters are afterwards tuned with the aid of the genetic algorithms (GAs) and the least square method (LSM). The overall design methodology arises as a hybrid development process involving structural and parametric optimization. Especially, genetic algorithms and C-Means are used to generate the structurally as well as parametrically optimized fuzzy model. To identify the structure and estimate parameters of the fuzzy model we exploit the methodologies such as joint and successive method realized by means of genetic algorithms. The proposed model is evaluated using experimental data and its performance is contrasted with the behavior of the fuzzy models available in the literature.     

Implicit rule-based fuzzy-neural networks using the identification algorithm of GA hybrid scheme based on information granulation

This paper proposes an identification method for nonlinear models realized in the form of implicit rule-based fuzzy-neural networks (FNN). The design of the model dwells on the technologies of computational intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithm. The FNN modeling and identification environment realizes parameter estimation through a synergistic usage of clustering techniques, genetic optimization and a complex search method. An HCM (Hard C-Means) clustering algorithm helps determine an initial location (parameters) of the membership functions of the information granules to be used in this fuzzy model. The parameters such as apexes of membership functions, learning rates, and momentum coefficients are then adjusted using the optimization algorithm of a GA hybrid scheme. The proposed GA hybrid scheme combines GA with the improved complex method to guarantee both global optimization and local convergence. An aggregate objective function (performance index) is used in the model design in order to achieve a sound balance between its approximation and generalization abilities. The proposed type of the model is experimented with several time series data (gas furnace, sewage treatment process, and NOx emission process data of gas turbine power plant).     

基于软分类和卡尔曼滤波方法的模糊规则提取

提出了一种新的基于遗传模糊软分类和卡尔曼滤波方法的模糊辨识算法.该算法由3个步骤组成：（1）基于遗传算法确定模糊C均值（FCM）中的最佳分类数,从而确定模糊规则的前件和样本在各类中的隶属度;（2）采用最小二乘法（LS）来确定模糊规则后件的初始参数;（3）用卡尔曼滤波方法调整后件参数.最后,运用该算法对我国全要素生产力进行了模糊规则的提取.     

Rule-based multi-FNN identification with the aid of evolutionary fuzzy granulation

In this paper, we introduce a category of Multi-Fuzzy-Neural Networks (Multi-FNNs) models, analyze the underlying architectures and propose a comprehensive identification framework. The proposed Multi-FNNs are based on a concept of fuzzy rule-based FNNs that use H ard C-M eans (HCM) clustering and evolutionary fuzzy granulation and exploit linear inference being treated as a generic inference mechanism of approximate reasoning. By this nature, this FNN model is geared toward capturing relationships between information granules–fuzzy sets. The form of the information granules themselves (in particular their distribution and a type of membership functions) becomes an important design feature of the FNN model that contributes to its structural and parametric optimization. The genetically guided global optimization is then augmented by more refined gradient-based learning mechanisms such as a standard back-propagation. The HCM algorithm, whose role is to carry out preprocessing of the experimental data, is utilized to determine the structure of Multi-FNNs. The detailed parameters of the Multi-FNN (such as apexes of membership functions, learning rates, and momentum coefficients) are adjusted using genetic algorithms. The proposed aggregate performance index helps achieve a sound balance between approximation and generalization (predictive) abilities of the model. To evaluate an effectiveness of the introduced model, several numeric data sets are experimented with. Those include a time-series data of gas furnace, NOx emission process of gas turbine power plant and some synthetic data.     

IG-based genetically optimized fuzzy polynomial neural networks with fuzzy set-based polynomial neurons

In this study, we introduce and investigate a new topology of fuzzy-neural networks—fuzzy polynomial neural networks (FPNN) that is based on a genetically optimized multiplayer perceptron with fuzzy set-based polynomial neurons (FSPNs). We also develop a comprehensive design methodology involving mechanisms of genetic optimization and information granulation. In the sequel, the genetically optimized FPNN (gFPNN) is formed with the use of fuzzy set-based polynomial neurons (FSPNs) composed of fuzzy set-based rules through the process of information granulation. This granulation is realized with the aid of the C-means clustering (C-Means). The design procedure applied in the construction of each layer of an FPNN deals with its structural optimization involving the selection of the most suitable nodes (or FSPNs) with specific local characteristics (such as the number of input variable, the order of the polynomial, the number of membership functions, and a collection of specific subset of input variables) and address main aspects of parametric optimization. Along this line, two general optimization mechanisms are explored. The structural optimization is realized via genetic algorithms (GAs) and HCM method whereas in case of the parametric optimization we proceed with a standard least square estimation (learning). Through the consecutive process of structural and parametric optimization, a flexible neural network is generated in a dynamic fashion. The performance of the designed networks is quantified through experimentation where we use two modeling benchmarks already commonly utilized within the area of fuzzy or neurofuzzy modeling.     

Application of fuzzy Naive Bayes and a real-valued genetic algorithm in identification of fuzzy model

We present a method to identify a fuzzy model from data by using the fuzzy Naive Bayes and a real-valued genetic algorithm. The identification of a fuzzy model is comprised of the extraction of “if–then” rules that is followed by the estimation of their parameters. The involved parameters include those which determine the membership function of fuzzy sets and the certainty factors of fuzzy if–then rules. In our method, as long as the fuzzy partition in the input–output space is given, the certainty factor of each rule is computed with the fuzzy conditional probability of the consequent conditioned on the antecedent by using the fuzzy Naive Bayes, which is a generalization of Naive Bayes. The fuzzy model involves the rules characterized by the highest values of certainty factors. The certainty factor of each rule is the fuzzy conditional probability, and it reflects the inner relationship between the antecedent and the consequent. In order to improve the accuracy of the fuzzy model, the real-valued genetic algorithm is incorporated into our identification process. This process concerns the optimization of the membership functions occurring in the rules. We just involve the parameters of membership function of the fuzzy sets into the real-valued genetic algorithm, since the certainty factor of each rule can be computed automatically. The performance of the model is shown for the backing-truck problem and the prediction of Mackey–Glass time series.     

Design of rule-based models through information granulation

In this study, we explore the combination of two well defined topics in fuzzy systems research: fuzzy rule based systems, and information granulation. Rule based systems are a powerful and well-studied form of knowledge representation, due to their approximation abilities and interpretability. In recent years, these types of systems have become increasingly powerful with regards to modeling accuracy; however, many of these improvements come at the cost of model interpretability. This recent direction of research has left an unexplored avenue towards the generation of increasingly interpretable fuzzy rule based models, which we intend to explore. Information granulation is a relatively new, yet very promising area of research in human centric systems. As a form of knowledge representation, information granulation is very well suited to fuzzy rule based systems, where rules represent linguistic quantities in a, intuitively understandable format. It is notable that the combination of these two concepts has been left largely unstudied. We aim to explore this union by defining a methodology for the construction of a partially granular fuzzy rule based model. The aim of this novel model format is to provide a first step in the improvement of fuzzy model interpretability, through the use of information granulation. We are additionally interested in studying new ways of generating fuzzy rules; hence, we will also look at the use of hierarchical clustering as a potential alternative to the tried and tested Fuzzy C Means clustering algorithm. The models created using hierarchical clustering are then compared with those generated using Fuzzy C Means to evaluate the effectiveness of this algorithm. As a result of these experiments, we demonstrate that partially granular fuzzy rules are capable of providing a significant improvement to fuzzy rule interpretability, and we believe that granular fuzzy models present an exciting avenue of future research in human centric systems.     

Type-2 fuzzy neural networks with fuzzy clustering and differential evolution optimization

In many real-world problems involving pattern recognition, system identification and modeling, control, decision making, and forecasting of time-series, available data are quite often of uncertain nature. An interesting alternative is to employ type-2 fuzzy sets, which augment fuzzy models with expressive power to develop models, which efficiently capture the factor of uncertainty. The three-dimensional membership functions of type-2 fuzzy sets offer additional degrees of freedom that make it possible to directly and more effectively account for model’s uncertainties. Type-2 fuzzy logic systems developed with the aid of evolutionary optimization forms a useful modeling tool subsequently resulting in a collection of efficient “If-Then” rules.The type-2 fuzzy neural networks take advantage of capabilities of fuzzy clustering by generating type-2 fuzzy rule base, resulting in a small number of rules and then optimizing membership functions of type-2 fuzzy sets present in the antecedent and consequent parts of the rules. The clustering itself is realized with the aid of differential evolution.Several examples, including a benchmark problem of identification of nonlinear system, are considered. The reported comparative analysis of experimental results is used to quantify the performance of the developed networks.     

Tuning of a neuro-fuzzy controller by genetic algorithm

Due to their powerful optimization property, genetic algorithms (GAs) are currently being investigated for the development of adaptive or self-tuning fuzzy logic control systems. This paper presents a neuro-fuzzy logic controller (NFLC) where all of its parameters can be tuned simultaneously by GA. The structure of the controller is based on the radial basis function neural network (RBF) with Gaussian membership functions. The NFLC tuned by GA can somewhat eliminate laborious design steps such as manual tuning of the membership functions and selection of the fuzzy rules. The GA implementation incorporates dynamic crossover and mutation probabilistic rates for faster convergence. A flexible position coding strategy of the NFLC parameters is also implemented to obtain near optimal solutions. The performance of the proposed controller is compared with a conventional fuzzy controller and a PID controller tuned by GA. Simulation results show that the proposed controller offers encouraging advantages and has better performance.     

Parameter determination for a generalized fuzzy model

This paper underlines a way to evolve a generalized fuzzy model (GFM), using the interpolation of CRI and TS models in their consequent parts of fuzzy rules. The GFM possesses the index of fuzziness of CRI model and the local model of the TS model. The parameters of the GFM are estimated by a two-step process. The consequent part of fuzzy rules is reformulated to suit the LSE framework for estimating the associated parameters. By assuming Generalized Gaussian membership function for the premise parts, Gradient descent technique is used to update its parameters. The performance of two classes of GFM has been tested on two systems and it is shown that class II GFM is the best out of all the fuzzy models tested.     

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.     

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．     

Fuzzy identification of a greenhouse

Nonlinear dynamic systems’ modelling is difficult. The solutions proposed are generally based on the linearization of the process behaviour around the operating points. Other researches were carried out on this technique of linearization not only around the operating points, but also in all the input–output space allowing the obtaining of several local linear models. The major difficulty with this technique is the model transition. Fuzzy logic makes it possible to solve this problem thanks to its properties of universal approximator. Indeed, many techniques of modelling and identification based on fuzzy logic are often used for this type of systems. Among these techniques, we find those based on the fuzzy clustering technique. The proposed method uses in a first stage the fuzzy clustering technique to determine both the premises and the consequent parameters of the fuzzy Takagi–Sugeno rules. In a second stage these consequent parameters are adapted by using the recursive weighted least squares algorithm with a forgetting factor. We will try in this paper to apply this method to model the air temperature and humidity inside the greenhouse.     

基于自组织神经网络的非线性系统建模

针对基于T-S模糊模型的非线性系统建模问题,提出了一种基于自组织神经网络的新方法.在T-S模糊模型的建模中,目前常用的模糊C均值聚类算法存在迭代次数多,计算耗时的缺点.首先,利用竞争学习算法对输入空间进行聚类,基于此结果,借助于模糊C均值聚类算法进一步优化聚类结果,提取T-S模糊模型的规则前件隶属函数参数.然后,采用最小二乘法求得T-S模糊模型的规则后件参数,从而建立起非线性系统的T-S模糊模型.最后,仿真结果表明,该方法可以为模糊建模提供好的模型结构,并且有较高的计算效率和精度.     

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.     

CLUSTERED BASED TAKAGI‐SUGENO NEURO‐FUZZY MODELING OF A MULTIVARIABLE NONLINEAR DYNAMIC SYSTEM

This research frame work investigates the application of a clustered based Neuro‐fuzzy system to nonlinear dynamic system modeling from a set of input‐output training patterns. It is concentrated on the modeling via Takagi‐Sugeno (T‐S) modeling technique and the employment of fuzzy clustering to generate suitable initial membership functions. Hence, such created initial memberships are then employed to construct suitable T‐S sub‐models. Furthermore, the T‐S fuzzy models have been validated and checked through the use of some standard model validation techniques (like the correlation functions). Compared to other well‐known approximation techniques such as artificial neural networks, fuzzy systems provide a more transparent representation of the system under study, which is mainly due to the possible linguistic interpretation in the form of rules. Such intelligent modeling scheme is very useful once making complicated systems linguistically transparent in terms of fuzzy if‐then rules. The developed T‐S Fuzzy modeling system has been then applied to model a nonlinear antenna dynamic system with two coupled inputs and outputs. Validation results have resulted in a very close antenna sub‐models of the original nonlinear antenna system. The suggested technique is very useful for development transparent linear control systems even for highly nonlinear dynamic systems.     

融合KL信息的多视图模糊聚类算法

现有多视图模糊C均值聚类（FCM）算法通常将一个多视图分解为多个单视图进行数据处理,导致视图数据聚类精度降低,从而影响全局数据划分结果。为实现高维数据和多视图数据的高效聚类,提出一种基于KL信息的多视图自加权模糊聚类算法。将多个视图信息及其权重进行拟合融入标准FCM算法,求解多个隶属度矩阵和质心矩阵。在此基础上,通过附加KL信息作为模糊正则项进一步修正共识隶属度矩阵并保持权重分布的平滑性,其中KL信息是视图隶属度与其共识隶属度的比值,最小化KL信息会使每个视图的隶属度偏向于共识隶属度以得到更好的聚类结果。实验结果表明,该算法相比于传统聚类算法具有更好的聚类效果和更快的收敛速度,尤其在3-Sources数据集上相比于MVASM算法的聚类精度、标准化互信息和纯度分别提升了7.46、15.34和5.48个百分点。     

Design of fuzzy PID controllers using modified triangular membership functions

A design method for fuzzy proportional-integral-derivative (PID) controllers is investigated in this study. Based on conventional triangular membership functions used in fuzzy inference systems, the modified triangular membership functions are proposed to improve a system’s performance according to knowledge-based reasonings. The parameters of the considered controllers are tuned by means of genetic algorithms (GAs) using a fitness function associated with the system’s performance indices. The merits of the proposed controllers are illustrated by considering a model of the induction motor control system and a higher-order numerical model.     

Fuzzy classifier design using genetic algorithms

A new method for design of a fuzzy-rule-based classifier using genetic algorithms (GAs) is discussed. The optimal parameters of the fuzzy classifier including fuzzy membership functions and the size and structure of fuzzy rules are extracted from the training data using GAs. This is done by introducing new representation schemes for fuzzy membership functions and fuzzy rules. An effectiveness measure for fuzzy rules is developed that allows for systematic addition or deletion of rules during the GA optimization process. A clustering method is utilized for generating new rules to be added when additions are required. The performance of the classifier is tested on two real-world databases (Iris and Wine) and a simulated Gaussian database. The results indicate that highly accurate classifiers could be designed with relatively few fuzzy rules. The performance is also compared to other fuzzy classifiers tested on the same databases.     

基于改进模糊聚类与ANFIS的高速公路事件检测

为了准确并及时地发现高速公路上的交通事故隐患,减少事故引发的交通延迟,提高高速公路运行安全性,结合减法聚类与模糊C均值（FCM）聚类算法对输入样本数据进行聚类,建成初始模糊推理系统,然后通过神经网络的自学习机制,训练模糊系统参数,确定模糊推理规则,建立最终模糊模型。通过仿真实验结果对比,验证了基于改进模糊聚类与自适应神经模糊推理系统（ANFIS）建模方法的有效性。