A class of hierarchical fuzzy systems with constraints on the fuzzy rules

This paper presents a class of hierarchical fuzzy systems where previous layer outputs are used not in IF-parts, but only in THEN-parts of the fuzzy rules of the current layer. The proposed scheme is shown to be a universal approximator to any real continuous function on a compact set if complete fuzzy sets are used in the IF-parts of the fuzzy rules with singleton fuzzifier and center average defuzzifier. From the example of ball-and-beam control system simulation, it is demonstrated that the proposed scheme approximates with high accuracy a model nonlinear controller with fewer fuzzy rules than a centralized fuzzy system, and its control performance is comparable to that of a nonlinear controller.     

Analysis and design of hierarchical fuzzy systems

In this letter, the hierarchical fuzzy systems are analyzed and designed. In the analysis part, we prove that the hierarchical fuzzy systems are universal approximators and analyze the sensitivity of the fuzzy system output with respect to small perturbations in its inputs. In the design part, we derive a gradient descent algorithm for tuning the parameters of the hierarchical fuzzy system to match the input-output pairs. The algorithm is simulated for two examples and the results show that the algorithm is effective and the hierarchical structure gives good approximation accuracy     

A control engineering review of fuzzy systems

Many complex industrial processes cannot be satisfactorily controlled using the results of modern control theory, mainly because their precise structure is unknown. However, this is often balanced by a considerable amount of ‘engineering feel’ for the process which is difficult to quantify and utilise. Fuzzy set theory is a relatively new concept which allows this qualitativeness to be expressed rigorously and in this paper its usefulness for control is assessed. The state of the art is reviewed and reveals a surprising number of practical successes.     

基于分层模糊系统的直接自适应控制

为解决模糊控制器中规则数目随系统变量呈指数增长的问题，利用分层模糊系统设计了一类非线性系统的直接自适应模糊控制器，并证明了所提出的设计方法不但能保证闭环系统的一致有界性。而且可使跟踪误差收敛到原点的小领域内，通过对倒立摆控制的仿真研究验证了该方法的有效性。     

广义递阶Mamdani模糊系统及其泛逼近性

从解决模糊系统的“规则爆炸”问题出发,本文首先给出广义递阶M amdan i模糊系统的定义,然后证明其与具有中间变量的广义M amdan i模糊系统等价,并借助方形分片线性函数构造性的证明了在最大模和积分模意义下该系统是泛逼近器.最后仿真实例证实了该系统的有效性.     

A fuzzy hierarchical reinforcement learning based scheduling method for semiconductor wafer manufacturing systems

Scheduling semiconductor wafer manufacturing systems has been viewed as one of the most challenging optimization problems owing to the complicated constraints, and dynamic system environment. This paper proposes a fuzzy hierarchical reinforcement learning (FHRL) approach to schedule a SWFS, which controls the cycle time (CT) of each wafer lot to improve on-time delivery by adjusting the priority of each wafer lot. To cope with the layer correlation and wafer correlation of CT due to the re-entrant process constraint, a hierarchical model is presented with a recurrent reinforcement learning (RL) unit in each layer to control the corresponding sub-CT of each integrated circuit layer. In each RL unit, a fuzzy reward calculator is designed to reduce the impact of uncertainty of expected finishing time caused by the rematching of a lot to a delivery batch. The results demonstrate that the mean deviation (MD) between the actual and expected completion time of wafer lots under the scheduling of the FHRL approach is only about 30 % of the compared methods in the whole SWFS.     

Incremental hierarchical construction of modular supervisors for discrete-event systems

Adoption of the supervisory control framework introduced by Ramadge and Wonham has been slowed somewhat by the problem of state space explosion that arises in systems of the scale common to most industrial applications. Hierarchical and modular approaches have been explored historically as means for addressing this problem. The limitations of these approaches include that a ‘consistent’ hierarchy is often difficult to achieve, and that modular supervisors often conflict with each other when acting in conjunction. This paper offers an approach that addresses some of these issues by incrementally building modular supervisors that are nonconflicting by construction. Abstractions are employed to make the procedure more computationally feasible. Proof is given showing the set of modular supervisors generated in this manner meet given specifications without blocking. Furthermore, examples are provided that demonstrate the reduction in complexity that this approach provides.     

基于递阶分解聚类的非线性系统递推模糊辨识

提出一种基于递阶分解聚类的递推模糊辨识方法．采用半模糊化方法对论域内的样本进行归类,根据各子集“线性化”程度评判模糊聚类的有效性,通过对性能最差的子集进行分解并辨识新增子模型的参数,逐步完成整个样本空间的模糊划分和模型辨识过程．在线辨识时采用递推最小二乘算法对模糊规则进行修正,同时可根据建模精度的要求删除性能最差的规则,并确立新模糊规则．仿真研究表明了该方法的有效性．     

Selection and impact of different topologies in multi-layered hierarchical fuzzy systems

An evolutionary algorithm based approach for selection of topologies in hierarchical fuzzy systems (HFS) is presented. Coupling fuzzy system with evolutionary algorithm provides a solution to the automated acquisition of the fuzzy rule base. It is difficult to study the problem of hierarchical decomposition for a large class of fuzzy systems but it is possible to analyse such architectures on the example of a particular fuzzy system, such as inverted pendulum. Topology of the HFS must be selected according to the physical properties of the dynamical system under consideration. Different HFS topologies for an inverted pendulum system are investigated and analysed to address the problem of how input configuration in multi-layered structure affects the controller performance. The experiments are conducted to test controller performance for different topologies of the hierarchical fuzzy system. The impact of different topologies on control process is discussed. The results from the case study of inverted pendulum can be extended to other dynamical systems.     

Multi-objective genetic learning of serial hierarchical fuzzy systems for large-scale problems

When we face a problem with a high number of variables using a standard fuzzy system, the number of rules increases exponentially and the obtained fuzzy system is scarcely interpretable. This problem can be handled by arranging the inputs in hierarchical ways. This paper presents a multi-objective genetic algorithm that learns serial hierarchical fuzzy systems with the aim of coping with the curse of dimensionality. By means of an experimental study, we have observed that our algorithm obtains good results in interpretability and accuracy with problems in which the number of variables is relatively high.     

基于减法聚类和自适应神经模糊推理系统的递阶模糊系统的设计

提出了一种设计递阶模糊系统的简易而有效的方法.在得到一个单级模糊系统的基础上,用灵敏度分析法对每一个输入变量的重要性进行排序,从而确定每一级子系统的输入变量.利用减法聚类和自适应神经 模糊推理系统逐级对子系统进行训练.所得到的递阶模糊系统可进一步得到简化.仿真实例证实了设计方法的有效性.     

A hierarchical approach to multi-class fuzzy classifiers

In this paper we present a hierarchical approach for generating fuzzy rules directly from data in a simple and effective way. The fuzzy classifier results from the union of fuzzy systems, employing the Wang and Mendel algorithm, built on input regions increasingly smaller, according to a multi-level grid-like partition. Key parameters of the proposed method are optimized by means of a genetic algorithm. Only the necessary partitions are built, in order to guarantee high interpretability and to avoid the explosion of the number of rules as the hierarchical level increases. We apply our method to real-world data collected from a photovoltaic (PV) installation so as to linguistically describe how the temperature of the PV panel and the irradiation relate to the class (low, medium, high) of the energy produced by the panel. The obtained mean and maximum classification percentages on 30 repetitions of the experiment are 97.38% and 97.91%, respectively. We also apply our method to the classification of some well-known benchmark datasets and show how the achieved results compare favourably with those obtained by other authors using different techniques.     

Self-nominating trust model based on hierarchical fuzzy systems for peer-to-peer networks

Security is a critical constraint for the expansion of Peer-to-Peer (P2P) networks. The autonomy, dynamic and distribution natures benefit both valid and malicious users and also lead that P2P networks are extremely susceptible to malicious users. Exploiting a reputation-based trust model is a feasible solution in such an open environment to build trust relationship among peers. While most of existing trust models focus on restraining the abuse and malicious attacks, intentions and sharing capabilities of peers are mostly ignored. In this paper, we present a self-nominating trust model based on hierarchical fuzzy systems to quantify the behaviors of peers. The reputation is defined based on eight factors, where three promising factors are provided by resource holders to demonstrate their desires, and four capability factors are recorded by requesters to identify the provider’s service capability. The approach degree based updating recommendation is deployed to aggregate the global trust metrics. Experimental results illustrate that our trust model effectively improves the efficiency and security of P2P systems.     

具有任意形状隶属函数的分层模糊系统逼近性能研究

首先证明了对任意给定的矩阵A和正数c, 一定存在向量b, 使得方程Ax=b有非负解, 且b和解的范数均小于c. 在此基础上证明了具有任意形状隶属函数的分层模糊系统对紧集上连续函数的逼近性质, 为使用分层模糊系统进行辨识或控制以避免模糊规则数目随系统变量个数呈指数增长提供了理论依据.     

Some algorithms for the construction of coordinated solutions in hierarchical distributed systems

Algorithms for constructing coordinated solutions in multilevel distributed systems are proposed. These algorithms utilize the nonformalizable knowledge of the decision maker about each subsystem and modify the set of feasible solutions of the local problems. Convergence of the proposed algoritms is proved.Translated from Kibernetika, No. 2, pp. 42–46, March–April, 1990.     

A fuzzy hierarchical operator in the grey wolf optimizer algorithm

The main goal of this paper is to study the performance of the Grey Wolf Optimizer (GWO) algorithm when a new hierarchical operator is introduced in the algorithm. This new operator is basically a hierarchical transformation that is inspired in the hierarchical social pyramid of the grey wolf. This proposed operator is applied to the simulation of the hunting process in the algorithm and has 5 variants that are explained in more detail in this paper (centroid, weighted, based on the fitness and two variants using fuzzy logic). Notably the variants having the greatest impact in the GWO performance are based on the use of fuzzy logic. We also present the motivation and results of experiments, as well as the benchmark functions that were used for the tests that are presented. In addition we are presenting a comparison among all methods for 30, 64 and 128 dimensions and we conclude that the performance of the Hierarchical GWO algorithm is better when using a fuzzy variant of the hierarchical operator.     

含模型不确定性移动机器人路径跟踪的分层模糊控制

对受非完整约束且含模型不确定性的移动机器人基于分层模糊系统设计了跟踪期望几何路径的鲁棒间接自适应控制方案.此方法除实现路径跟踪外,还可避免控制器的奇异性并保证跟踪方向.由于控制结构中使用了分层模糊系统,大大减少了模糊规则数目;并用鲁棒控制项对模糊系统逼近误差进行补偿,减少了其对跟踪精度的影响.证明了闭环系统跟踪误差收敛到原点的小邻域内,且可通过适当增大鲁棒控制项的设计参数使跟踪误差进一步减小.最后用实验结果验证了方法的有效性.     

A new method for fuzzy information retrieval based on fuzzy hierarchical clustering and fuzzy inference techniques

In this paper, we extend the work of Kraft et al. to present a new method for fuzzy information retrieval based on fuzzy hierarchical clustering and fuzzy inference techniques. First, we present a fuzzy agglomerative hierarchical clustering algorithm for clustering documents and to get the document cluster centers of document clusters. Then, we present a method to construct fuzzy logic rules based on the document clusters and their document cluster centers. Finally, we apply the constructed fuzzy logic rules to modify the user's query for query expansion and to guide the information retrieval system to retrieve documents relevant to the user's request. The fuzzy logic rules can represent three kinds of fuzzy relationships (i.e., fuzzy positive association relationship, fuzzy specialization relationship and fuzzy generalization relationship) between index terms. The proposed fuzzy information retrieval method is more flexible and more intelligent than the existing methods due to the fact that it can expand users' queries for fuzzy information retrieval in a more effective manner.