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.     

基于共享最近邻聚类和模糊集理论的分类器

提出一种基于共享最近邻聚类和模糊集理论的分类器．首先,在提出与核点密切相关的核半径概念的基础上,应用共享最近邻聚类得到正常类空间的部分核点和核半径,建立求解正常类空间补充核点的多目标优化模型,从而获得刻画正常类空间的全部核点和核半径．然后,将模糊集理论引入正常类的类属划分中,利用核点和核半径定义正常类的隶属度函数,建立基于隶属度函数的分类函数或分类器．实验表明,该分类器能处理包含噪音、孤立点和不规则子类的高维数据集的分类问题．     

饱和时滞非线性系统的间接线性矩阵不等式抗饱和设计

当时滞非线性系统具有执行器饱和时,其稳定性无法得到保证.为了寻找饱和时滞非线性系统的稳定控制器,本文阐述了一种间接线性矩阵不等式(LMI)一步抗饱和设计方法.首先,利用Takagi-Sugeno (T–S)模糊模型将一类饱和时滞非线性系统精确重构,引入输出反馈并行分布补偿系统得到闭环控制系统.然后,运用李雅普诺夫稳定性理论,导出闭环系统的稳定条件,利用一个矩阵不等式的等价引理,将闭环系统稳定条件间接的转化为两个LMIs条件,进而得到间接LMI抗饱和补偿算法,同时给出了吸引域估计及其优化模型.最后给出了应用此方案的一个仿真实例.     

Takagai-Sugeno模糊模型的并行分布补偿:新的稳定条件和动态反馈设计

讨论可以用Trakagai-Sugeno模糊模型描述的系统的补偿器设计.这种被称之为并行分布补偿(PDC)的控制器是基于参数并且影像了Trakagai-Sugeno模型的结构.通过引进动态并行分布控制(DPDC)的概念,扩展了关于此类控制器状态反馈的已有结果.提出三个新的结果.第一个结果给出了以往结果的宽松条件.这种条件是存在二次型稳定状态反馈这类控制器的充分条件.第二个结果给出了类似的二次型稳定动态反馈控制器存在的充分条件.第三个结果适用于Takagai-Sugeno模糊模型的基于性能的控制器设计.     

Box-Jenkins模型偏差补偿方法与其他辨识方法的比较

对于存在相关噪声干扰的Box—Jenkins系统,本文借助于偏差补偿原理,推导了一个偏差补偿最小二乘(BCLS)辨识方法;理论分析说明BCLS方法能够给出系统模型参数的无偏估计,并将提出的方法与递推增广最小二乘算法和递推广义增广最小二乘算法进行了比较研究;用仿真试验分析了这些算法的各自特点和适用范围。     

Takagai-Sugeno模糊模型的并行分布补偿:新的稳定条件和动态反馈设计(英文)

讨论可以用 Ｔａｋａｇａｉ－Ｓｕｇｅｎｏ模糊模型描述的系统的补偿器设计．这种被称之为并行分布补偿（ＰＤＣ）的控制器是基于参数并且影像了 Ｔａｋａｇａｉ－Ｓｕｇｅｎｏ模型的结构．通过引进动态并行分布控制（ＤＰＤＣ）的概念,扩展了关于此类控制器状态反馈的已有结果．提出三个新的结果．第一个结果给出了以往结果的宽松条件．这种条件是存在二次型稳定状态反馈这类控制器的充分条件．第二个结果给出了类似的二次型稳定动态反馈控制器存在的充分条件．第三个结果适用于 Ｔａｋａｇａｉ－Ｓｕｇｅｎｏ模糊模型的基于性能的控制器设计．     

基于聚类和遗传算法的解释性模糊模型设计

提出了一种基于模糊聚类和遗传算法构建解释性模糊模型的设计方法。定义了模糊模型的精确性指标,给出了模糊模型解释性的必要条件。然后利用模糊聚类算法和最小二乘法辨识初始的模糊模型;采用多目标遗传算法优化模糊模型;为提高模型的解释性,在遗传算法中利用基于相似性的模糊集合和模糊规则的简化方法对模型进行约简。采用该方法对Mackey-Glass系统进行建模,仿真结果验证了该方法的有效性。     

hGA: Hybrid genetic algorithm in fuzzy rule-based classification systems for high-dimensional problems

The aim of this work is to propose a hybrid heuristic approach (called hGA) based on genetic algorithm (GA) and integer-programming formulation (IPF) to solve high dimensional classification problems in linguistic fuzzy rule-based classification systems. In this algorithm, each chromosome represents a rule for specified class, GA is used for producing several rules for each class, and finally IPF is used for selection of rules from a pool of rules, which are obtained by GA. The proposed algorithm is experimentally evaluated by the use of non-parametric statistical tests on seventeen classification benchmark data sets. Results of the comparative study show that hGA is able to discover accurate and concise classification rules.     

Fuzzy adaptive genetic algorithms: design,taxonomy, and future directions

The genetic algorithm behaviour is determined by the exploitation and exploration relationship kept throughout the run. Adaptive genetic algorithms, that dynamically adjust selected control parameters or genetic operators during the evolution have been built. Their objective is to offer the most appropriate exploration and exploitation behaviour to avoid the premature convergence problem and improve the final results. One of the adaptive approaches are the adaptive parameter setting techniques based on the use of fuzzy logic controllers, the fuzzy adaptive genetic algorithms (FAGAs). In this paper, we analyse the FAGAs in depth. First, we describe the steps for their design and present an instance, which is studied from an empirical point of view. Then, we propose a taxonomy for FAGAs, attending on the combination of two aspects: the level where the adaptation takes place and the way the Rule-Bases are obtained. Furthermore, FAGAs belonging to different groups of the taxonomy are reviewed. Finally, we identify some open issues, and summarise a few new promising research directions on the topic. From the results provided by the approaches presented in the literature and the experimental results achieved in this paper, an important conclusion is obtained: the use of fuzzy logic controllers to adapt genetic algorithm parameters may really improve the genetic algorithm performance. This research has been supported by DGICYT PB98-1319.     

Fuzzy regression analysis: Systematic review and bibliography

Statistical regression analysis is a powerful and reliable method to determine the impact of one or several independent variable(s) on a dependent variable. It is the most widely used of all statistical methods and has broad applicability to numerous practical problems. However, various problems can arise, when for instance the sample size is too small, distributional assumptions are not fulfilled, the relationship between independent and dependent variables is vague or when there is an ambiguity of events. Moreover, the complexity of real-life problems often makes the underlying models inadequate, since information is frequently imprecise in many ways. To relax these rigidities, numerous researchers have modified and extended concepts of statistical regression analysis by means of concepts of fuzzy set theory. By now, there is a large number of papers on the topic of fuzzy regression analysis, especially concerning possibilistic, fuzzy least squares or machine learning approaches. Additionally, the variety of approaches includes probabilistic, logistic, type-2 and clusterwise fuzzy regression methods, among many others. Besides papers mainly devoted to advances in methodology, there are also several papers presenting case studies in various research fields. To structure this diversity of papers, proposals and applications we give in this paper a comprehensive systematic review and provide a bibliography on the topic of fuzzy regression analysis. Thus, the paper intends to consolidate the topic in order to aid new researchers in this area, focuses the field’s attention on key open questions, and highlights possible directions for future research.     

Robust stability and stabilizing controller design of fuzzy systems with discrete and distributed delays

In this paper, we consider delay-dependent stability conditions of Takagi-Sugeno fuzzy systems with discrete and distributed delays. Although many kinds of stability conditions for fuzzy systems with discrete delays have already been obtained, almost no stability condition for fuzzy systems with distributed delays has appeared in the literature. This is also true in case of the robust stability for uncertain fuzzy systems with distributed delays. Here we employ a generalized Lyapunov functional to obtain delay-dependent stability conditions of fuzzy systems with discrete and distributed delays. We introduce some free weighting matrices to such a Lyapunov functional in order to reduce the conservatism in stability conditions. These techniques lead to generalized and less conservative stability conditions. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques made on the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed delays. Moreover, we consider the state feedback stabilization. Based on stability and robust stability conditions, we obtain conditions for the state feedback controller to stabilize the fuzzy time-delay systems. Finally, we give two examples to illustrate our results. Delay-dependent stability conditions obtained here are shown to guarantee a wide stability region.     

Fuzzy Modeling Based on Ordinary Fuzzy Partitions and Nearest Neighbor Clustering

In this paper a novel algorithm is proposed to train fuzzy models. The novelty of the contribution lies on the development of a nearest neighbor-clustering scheme, which is able to perform the structure identification and the model parameter estimation without taking into account any random initial guesses. This nearest neighbor-clustering search is based on defining ordinary fuzzy partitions in the input space, and produces a number of spherical-shaped fuzzy clusters. The number of these clusters provides the number of rules of the fuzzy model. The premise model parameters are obtained by projecting the spherical clusters on each axe. Relationally, the consequent model parameters are determined by applying the orthogonal least-squares algorithm. Finally, the above model parameters are fine tuned by using the gradient descent method. The whole scheme requires one-pass through the data set and therefore it is a fast procedure that is easy to implement. Simulation experiments verify the algorithm's efficiency with respect to its prediction performance, its initialization capabilities, and its speed.     

Improving the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets and genetic amplitude tuning

Among the computational intelligence techniques employed to solve classification problems, Fuzzy Rule-Based Classification Systems (FRBCSs) are a popular tool because of their interpretable models based on linguistic variables, which are easier to understand for the experts or end-users.The aim of this paper is to enhance the performance of FRBCSs by extending the Knowledge Base with the application of the concept of Interval-Valued Fuzzy Sets (IVFSs). We consider a post-processing genetic tuning step that adjusts the amplitude of the upper bound of the IVFS to contextualize the fuzzy partitions and to obtain a most accurate solution to the problem.We analyze the goodness of this approach using two basic and well-known fuzzy rule learning algorithms, the Chi et al.’s method and the fuzzy hybrid genetics-based machine learning algorithm. We show the improvement achieved by this model through an extensive empirical study with a large collection of data-sets.     

On optimal experiment design for identifying premise and conclusion parameters of Takagi-Sugeno models: Nonlinear regression case

Optimal Experiment Design (OED) is a well-developed concept for regression problems that are linear-in-the-parameters. In case of experiment design to identify nonlinear Takagi-Sugeno (TS) models, non-model-based approaches or OED restricted to the local model parameters (assuming the partitioning to be given) have been proposed. In this article, a Fisher Information Matrix (FIM) based OED method is proposed that considers local model and partition parameters. Due to the nonlinear model, the FIM depends on the model parameters that are subject of the subsequent identification. To resolve this paradoxical situation, at first a model-free space filling design (such as Latin Hypercube Sampling) is carried out. The collected data permits making design decisions such as determining the number of local models and identifying the parameters of an initial TS model. This initial TS model permits a FIM-based OED, such that data is collected which is optimal for a TS model. The estimates of this first stage will in general not be ideal. To become robust against parameter mismatch, a sequential optimal design is applied. In this work the focus is on D-optimal designs. The proposed method is demonstrated for three nonlinear regression problems: an industrial axial compressor and two test functions.     

Fuzzy hypercubes: Linguistic learning/reasoning systems for intelligent control and identification

This paper introduces a new tool for intelligent control and identification. A robust and reliable learning and reasoning mechanism is addressed based upon fuzzy set theory and fuzzy associative memories. The mechanism storesa priori an initial knowledge base via approximate learning and utilizes this information for identification and control via fuzzy inferencing. This architecture parallels a well-known scheme in which memory implicative rules are stored disjunctively. We call this process afuzzy hypercube. Fuzzy hypercubes can be applied to a class of complex and highly nonlinear systems which suffer from vagueness uncertainty and incomplete information such as fuzziness and ignorance. Evidential aspects of a fuzzy hypercube are treated to assess the degree of certainty or reliability. The implementation issue using fuzzy hypercubes is raised, and finally, a fuzzy hypercube is applied to fuzzy linguistic control.     

一种模糊辨识方法及其在电站仿真器中的应用

利用模糊聚类和最小二乘估计方法提出一种糊辨识方法。该方法是基于模糊聚类,计算给定样本在各类中的隶属度,并利用递推最小二乘估计辨识模糊模型的后件参数。采用该方法对火力发电厂电站仿真器中的汽轮发电机密封油冷却系统进行建模研究,取得了满意的效果。     

Hybrid adaptive predictive control for the multi-vehicle dynamic pick-up and delivery problem based on genetic algorithms and fuzzy clustering

In this paper, we develop a family of solution algorithms based upon computational intelligence for solving the dynamic multi-vehicle pick-up and delivery problem formulated under a hybrid predictive adaptive control scheme. The scheme considers future demand and prediction of expected waiting and travel times experienced by customers.     

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.     

Data-driven and adaptive control applications to a wind turbine benchmark model

Wind turbines are complex dynamic systems forced by stochastic wind disturbances, as well as gravitational, centrifugal, and gyroscopic loads. Since their aerodynamics are nonlinear, wind turbine modelling is thus challenging. Moreover, accurate models should contain many degrees of freedom to capture the most important dynamic effects. Therefore, the design of control algorithms for wind turbines should account for these complexities. However, these algorithms must capture the most important turbine dynamics without being too complex and unwieldy. The main purpose of this study is thus to give two examples of viable and practical designs of control schemes with application to a wind turbine prototype model. Extensive simulations on the benchmark process and Monte-Carlo analysis are the tools for assessing experimentally the main features of the proposed control schemes, in the presence of modelling and measurement errors. These developed control methods are also compared with other different approaches, in order to evaluate advantages and drawbacks of the considered solutions. Finally, Hardware-In-the-Loop simulations serve to highlight the potential application of the proposed control strategies to real wind turbines.     

Fuzzy c-means: Optimality of solutions and effective termination of the algorithm

In this paper, the solutions produced by the fuzzy c-means algorithm for a general class of problems are examined and a method to test for the local optimality of such solutions is established. An equivalent mathematical program is defined for the c-means problem utilizing a generalized norm, then the properties of the resulting optimization problem are investigated. It is shown that the gradient of the resulting objective function at the solution produced by the c-means algorithm in this case takes a special structure which can be used in terminating the algorithm. Moreover, the local optimality of the solution obtained is checked utilizing the Hessian of the criterion function. The solution is a local minimum point if the Hessian matrix at this point is positive semidefinite. Simple rules are proposed to help in checking the definiteness of the matrix.