广义分层混合模糊系统及其泛逼近性

为避免广义模糊系统出现规则爆炸现象, 引进实参数将Mamdani模糊系统和T--S模糊系统统一起来建立广义分层混合模糊系统, 进而给出了广义分层混合模糊系统的数学表示. 此外, 应用方形分片线性函数的优良性质获得该广义分层混合模糊系统在积分模意义下仍具有泛逼近性, 并通过实例及仿真说明该分层混合模糊系统能够避免模糊规则爆炸问题.     

Hierarchical fuzzy relational models: linguistic interpretation and universal approximation

Hierarchical fuzzy structures composed of a series of sub-models connected in cascade have been found to be effective tools for dealing with the dimensionality problem in fuzzy systems. This paper addresses both the issues of linguistic interpretation and universal approximation of systems using hierarchical fuzzy models. Fuzzy relational equations are used to implement the sub-models of a hierarchical structure that has two very important properties: i) it can be converted into a completely equivalent nonhierarchical model, which in turn allows the extraction of linguistic knowledge in the form of consistent fuzzy If-Then rules; and ii) it is a universal approximator. These properties are analytically derived and the proposed model is illustrated by means of an example.     

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.     

分层云不确定推理系统及其逼近性能分析

为了解决目前基于云模型的智能控制和预测中规则数目随系统变量的个数呈指数增长的问题,设计分层云不确定性推理系统,并证明该系统的逼近性能。采用基于云理论的新的不确定性推理模型来设计分层云不确定性推理系统并给出解析表达式。证明分层云不确定性推理系统对致密集上函数的逼近能力。结果表明：分层云不确定性推理系统的输出结果计算式满足Stone-Weirstrass定理的3个假设条件,具有万能逼近性质。     

模糊系统万能逼近理论研究综述

模糊系统通用逼近理论是模糊理论研究的一个重要方向．目前，对模糊系统通用逼近性的研究已经取得了很大的进展．对模糊系统的通用逼近性、模糊系统作为通用逼近器的充分条件和必要条件以及模糊系统的逼近精度等方面的研究进行了较为详尽的综述，分析了各种分析方法的主要成果及其特点（包括优点和局限性），并指出了今后模糊系统通用逼近理论研究中有待解决的许多问题．     

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.     

A new approach for stabilizing a TS model fuzzy system

This paper presents a new approach to stabilizing a Takagi–Sugeno (TS) fuzzy model. A new controller design called proportional parallel distributed compensation (PPDC) is proposed. Different from other works, PPDC parameters are proportioned, which result in dramatic reduction in control parameters. In our new design, based on the Lyapunov stability analysis, the solution of finding the common positive definite matrix P is simplified and proportional coefficients design can be separated from feedback matrix parameters. Numerical simulation results show that the PPDC's performance is superior to that of PDC. This new approach has promising potential in practical applications of fuzzy systems. © 2001 John Wiley & Sons, Inc.     

A novel fuzzy neural network and its approximation capability

The polygonal fuzzy numbers are employed to define a new fuzzy arithmetic. A novel ex-tension principle is also introduced for the increasing function σ:R→R. Thus it is convenient to con-struct a fuzzy neural network model with succinct learning algorithms. Such a system possesses some universal approximation capabilities, that is, the corresponding three layer feedforward fuzzy neural networks can be universal approximators to the continuously increasing fuzzy functions.     

A new universal approximation result for fuzzy systems,which reflects CNF DNF duality

There are two main fuzzy system methodologies for translating expert rules into a logical formula: In Mamdani's methodology, we get a DNF formula (disjunction of conjunctions), and in a methodology which uses logical implications, we get, in effect, a CNF formula (conjunction of disjunctions). For both methodologies, universal approximation results have been proven which produce, for each approximated function f(x), two different approximating relations R_DNF(x, y) and R_CNF(x, y). Since, in fuzzy logic, there is a known relation F_CNF(x) ≤ F_DNF(x) between CNF and DNF forms of a propositional formula F, it is reasonable to expect that we would be able to prove the existence of approximations for which a similar relation R_CNF(x, y) ≤ R_DNF(x, y) holds. Such existence is proved in our paper. © 2002 Wiley Periodicals, Inc.     

Hierarchical wavelet packet fuzzy inference system for pattern classification and system identification

This study presents a hierarchical Takagi–Sugeno–Kang type fuzzy system called hierarchical wavelet packet fuzzy inference system. In the proposed method, wavelet packet transform is applied on the input data to produce approximation and detail sub-bands of the input data and the output is used as the input vector of the proposed network. This network uses a hierarchical structure same as wavelet packet decomposition tree, in which adaptive network-based fuzzy inference system is used as sub-model. Also, gradient descent algorithm is chosen for training the parameters of antecedent and conclusion parts of the sub-models. In order to evaluate the capability of the proposed method, its applications in pattern classification, system identification and time-series prediction have been studied. The results show that the proposed method performs better than the other conventional models.     

基于后件直联型分层的广义混合模糊系统及其积分模逼近

首先, 引入后件直联型分层方法及其推理规则, 以对广义混合模糊系统的输入变量实施分层, 获得分层广义混合模糊系统的输入输出表达式和推理规则数的计算公式; 然后, 基于??- 积分模(度量) 和分片线性函数证明分层后广义混合模糊系统对一类可积函数具有逼近性; 最后, 通过模拟实例给出后件直联型分层广义混合模糊系统对可积函数的逼近过程. 模拟结果表明, 所提出的方法不仅能使原系统模糊规则总数大大减少, 而且能使分层后系统仍具有逼近性.

     

Hierarchical fuzzy control

In a conventional rule based fuzzy control system, the rules are of the following form: if (condition) then (action), and all rules are essentially in a random order. The number of rules increases exponentially as the number of the system variables, on which the fuzzy rules are based, is increased. In this paper, the rules are structured in a hierarchical way so that the total number of rules will be a linear function of the system variables. The hierarchical fuzzy control algorithm developed in this paper is applied to control the feedwater flow to a steam generator of a power plant. The simulation results show that the hierarchical fuzzy controller yields superior performance over the conventional PID controller.     

On fuzzy equality and approximation in fuzzy logic

The paper is a contribution to the theory of fuzzy logic in narrow sense with evaluated syntax (FLn). We show that the concepts of fuzzy equality and the provability degree enable to generalize the concept of fuzzy approximation. In the second part of the paper we return to the Mamdani-Assilian formula, which is formed on the basis of the so called totally bounded fuzzy equality and using which we can approximate any function with the prescribed accuracy.This paper has been supported by Grant A1187901/99 of the GA AV R and the project VS96037 of MMT of the Czech Republic.     

植物运动的层次式简化技术

利用力学预计算方法生成植物运动的真实感动画需要对形变数据作有效简化和压缩。针对植物及其运动天然具有层级性的特点,提出一种基于视觉感知层次的动态几何简化算法。依据植物的树型层级结构,将各级“子树”的运动作高低频分解;“低频运动”表征“子树”的主体运动,“高频运动”即为运动细节。按“广度优先”遍历植物层级结构,在某一“深度”（层级）上将所有“子树”的“低频运动”合成即获得原始运动在此层次的逼近。遍历深度递增将构成植物运动的渐进逼近;递减则为植物运动的逐步抽象化,这实质上实现了植物运动的细节层次控制。实验表明该算法可实现植物运动的高效简化和压缩,利于生成大规模植物场景的真实感动画。     

Hierarchical unsupervised fuzzy clustering

A recursive algorithm for hierarchical fuzzy partitioning is presented. The algorithm has the advantages of hierarchical clustering, while maintaining fuzzy clustering rules. Each pattern can have a nonzero membership in more than one subset of the data in the hierarchy. Optimal feature extraction and reduction is optionally reapplied for each subset. Combining hierarchical and fuzzy concepts is suggested as a natural feasible solution to the cluster validity problem of real data. The convergence and membership conservation of the algorithm are proven. The algorithm is shown to be effective for a variety of data sets with a wide dynamic range of both covariance matrices and number of members in each class     

Positive approximation and converse approximation in interval-valued fuzzy rough sets

Methods of fuzzy rule extraction based on rough set theory are rarely reported in incomplete interval-valued fuzzy information systems. Thus, this paper deals with such systems. Instead of obtaining rules by attribute reduction, which may have a negative effect on inducting good rules, the objective of this paper is to extract rules without computing attribute reducts. The data completeness of missing attribute values is first presented. Positive and converse approximations in interval-valued fuzzy rough sets are then defined, and their important properties are discussed. Two algorithms based on positive and converse approximations, namely, mine rules based on the positive approximation (MRBPA) and mine rules based on the converse approximation (MRBCA), are proposed for rule extraction. The two algorithms are evaluated by several data sets from the UC Irvine Machine Learning Repository. The experimental results show that MRBPA and MRBCA achieve better classification performances than the method based on attribute reduction.     

Mamdani fuzzy system: universal approximator to a class of random processes

The issue of fuzzy systems as universal approximators has drawn significant attention, but all results obtained are restricted to deterministic input-output (I/O) relationships. It should be noted that, in practice, many I/O systems, including fuzzy systems, operate in the environment which is essentially stochastic. In this paper, the Mamdani fuzzy systems are generalized as stochastic systems. By proving the Mamdani systems as universal approximators with L/sup 2/-norm, the approximation capability of the stochastic Mamdani systems to a class of random processes is systematically analyzed. In the mean square sense, such stochastic fuzzy systems are capable of approximating the prescribed random processes with arbitrary accuracy. Further, an efficient learning algorithm for the stochastic Mamdani systems is developed. Finally, a simulation example is employed to demonstrate our results.     

Preference ratio-based maximum operator approximation and its application in fuzzy flow shop scheduling

Maximum operator distorts the shape(s) of Triangular Fuzzy Numbers (TFNs) and Trapezoidal Fuzzy Numbers (TrFNs) in many problems such as Flow shop scheduling, job-shop scheduling and project scheduling. In this paper, we introduce an appropriate approximation for the maximum operator, in which the weak-dominance fuzzy numbers are ranked based on the concept of preference ratio. Since in most practical cases the due dates and the processing time of scheduling are not deterministic, we consider the scheduling problems with fuzzy processing time. Finally we develop a novel fuzzy CDS algorithm in fuzzy flow shop scheduling by applying the preference ratio concept through an example.     

T-S模糊系统的构造及其逼近能力的充分条件

针对任意多变量非线性函数, 至今缺少一种简单有效的构造性方法来建造一个T-S模糊系统对其实现给定精度的模糊逼近. 本文在逼近函数g(X)∈C2及g(X)不∈C2两种情况下给出了一种当模糊集满足均匀性、连续性、正规性条件下T-S模糊系统的构造方法以及该T-S模糊系统逼近能力的充分条件. 该构造性方法简单易行且其逼近能力充分条件的保守性低. 最后通过仿真研究证实了该方法的正确性与有效性.