具有广义线性隶属函数的典型模糊系统的通用逼近性*

设计了一种将三角形和梯形隶属函数作为特例的广义线性隶属函数,推导了输入采用广义线性隶属函数的典型Mamdani模糊系统的解析结构,证明了典型模糊系统是单调、递减的有界连续函数;在此基础上证明了该类模糊系统能以任意精度逼近任意连续实函数,最后仿真实例证明了本设计的有效性。     

一种新型分层模糊系统及其逼近性能

针对分层模糊系统,提出一种新的结构形式,该分层模糊系统将各层中间变量作为后一层模糊单元输出结果中的一部分,而不再是输入项,这样不仅能够减少规则数目和辨识参数,而且避免了对不具物理含义的中间变量的模糊处理。给出新型分层模糊系统的解析表达式,证明了该分层模糊系统具有通用逼近性能,并给出存在性定理和逼近性能的充分条件。通过实例仿真表明所提出分层模糊系统具有较好的应用基础。     

偏序关系中盖住集的判定

直接根据现有离散数学教材中偏序关系中"盖住"的定义,来判定偏序关系中的盖住集,有时比较困难.文中通过对教材中偏序关系中"盖住"定义的深入分析,将定义"对于任意a,b∈A,当＜a,b＞∈R,a≠b且没有其它元素c满足＜a,c＞∈R和＜c,b＞∈R,则称元素b盖住元素a,并且记COVR={＜a,b＞| a,b∈A;b盖住a }"改为"对于任意＜a,b＞∈R且a=b,则＜a,b＞∈IR,令R1=R-IR,则R1-(R1○R1)为盖住集",得出一种等价的定义形式.利用该等价定义可以较好地实现盖住集的判定.     

一般齐次T-S模糊系统的逼近性能

为剖析一般齐次T-S模糊系统的逼近性能,通过广泛总结常用模糊集的特点,明确定义了一种具有普遍意义的输入空间的一般模糊划分(GFP).基于输入采用GFP的一般齐次T-S模糊系统的解析结构,证明了该类一般齐次T-S模糊系统能够以任意精度逼近任意非线性函数,并得到了一个其作为通用逼近器的充分条件.作为GFP的一种退化,进一步研究了输入采用线性模糊划分(LFP)的一般齐次T-S模糊系统的一阶逼近性能.仿真实例验证了所得理论结果的有效性,并考察了充分条件的保守性.这为基于齐次T S模糊模型的复杂系统建模与控制提供了理论指导.     

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.     

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.     

复杂系统模糊建模的模糊树方法

对含高度非线性的复杂系统的模糊建模提出了一种二叉线性模糊树方法. 证明了对n维空间中任一闭集上有限样本集或连续函数, 总存在模糊树模型以任一精度逼近之. 模糊树模型在一定程度上模拟了对复杂问题进行分层、分段简化决策的思维过程, 故对其进一步的研究具有科学与应用价值.     

模糊数学在计算机工程中的应用(二)——模糊聚类分析及其实际应用

一、模糊关系概述在叙述模糊关系、模糊矩阵等概念之前,首先简要地复习一下通常的关系和关系之间的复合,以及用普通集合论中的特征函数来描述的二元关系和关系之间的复合。简单地讲,序对是指二个元素a和b的有序对,记作(a,b),序对(a,b)与序对(c,d)相等是指 a=c,b=d。     

模糊图上合作对策的平均树解

针对模糊图上的平均树解进行研究.在无向模糊图中,参与者本身与参与者之间有不同的参与水平,利用Choquet积分函数对模糊图进行划分,定义模糊平均树解,并证明它是满足模糊分支有效性和cg分支公平性的唯一解,以及满足模糊分支有效性和模糊分支公平性的唯一解.此外,当无圈模糊图合作对策满足超可加性时,证明模糊平均树解是核中的元素,即该解是稳定的.利用Choquet积分函数和深度搜索算法(DFS)将无圈图上的模糊平均树解推广到任意图上,拓展了任意图上模糊平均树解的表达形式.最后,通过一个供应链算例计算并分析模糊图上合作对策的平均树解.     

基于二叉树型分层的广义混合模糊系统推理规则数的缩减

为避免广义混合模糊系统因输入变量个数的增加而引起规则爆炸现象,应用二叉树型分层方法给出混合推理规则,进而对广义混合模糊系统的输入实施二叉树型分层,从理论上获得了该系统分层后的输入输出表达式和推理规则总数的计算公式.此外,通过实例对该系统分层和不分层的规则总数进行了比较和分析,结果表明分层后广义混合模糊系统可大幅度缩减推理规则总数,并可有效地避免规则爆炸.     

Hierarchical Fuzzy Systems for Function Approximation on Discrete Input Spaces With Application

This paper investigates the capabilities of hierarchical fuzzy systems to approximate functions on discrete input spaces. First, it is shown that any function on a discrete space has an arbitrary separable hierarchical structure and can be naturally approximated by hierarchical fuzzy systems. As a by-product of this result, a discrete version of Kolmogorov's theorem is obtained; second, it is proven that any function on a discrete space can be approximated to any degree of accuracy by hierarchical fuzzy systems with any desired separable hierarchical structure. That is, functions on discrete spaces can be approximated more simply and flexibly than those on continuous spaces; third, a hierarchical fuzzy system identification method is proposed in which human knowledge and numerical data are combined for system construction and identification. Finally, the proposed method is applied to the market condition performance modeling problem in site selection decision support and shows the better performance in both accuracy and interpretability than the regression and neural network approaches. In additions, the reason and mechanism why hierarchical fuzzy systems outperform regression and neural networks in this type of application are analyzed.      

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.     

Approximation Capabilities of Hierarchical Fuzzy Systems

Derived from practical application in location analysis and pricing, and based on the approach of hierarchical structure analysis of continuous functions, this paper investigates the approximation capabilities of hierarchical fuzzy systems. By first introducing the concept of the natural hierarchical structure, it is proved that continuous functions with natural hierarchical structure can be naturally and effectively approximated by hierarchical fuzzy systems to overcome the curse of dimensionality in both the number of rules and parameters. Then, based on Kolmogorov's theorem, it is shown that any continuous function can be represented as a superposition of functions with the natural hierarchical structure and can then be approximated by hierarchical fuzzy systems to achieve the universal approximation property. Further, the conditions under which the hierarchical fuzzy approximation is superior to the standard fuzzy approximation in overcoming the curse of dimensionality are analyzed     

Closed-form solution for reliability of SCI-based multiprocessor systems using Weibull distribution and self-healing rings

This paper introduces a new closed-form solution for the reliability of large-scale multiprocessor systems. The systems are based on SCI rings interconnected in hierarchical structures. Reliability expressions using enumeration technique are derived assuming Weibull failure process. The reliability function derived in this paper is general and valid for any hierarchical ring-based system with arbitrary number of levels. The hierarchical interconnections are constructed from self-healing rings and basic rings. The analysis shows the improvement achieved in reliability when self-healing rings are used. Although we used hierarchical systems based on SCI rings, the technique followed in this work is applied for any type of rings such as slotted or token rings.     

Approximation capabilities of hierarchical hybrid systems

This paper investigates the approximation capabilities of hierarchical hybrid systems, which are motivated by research in hierarchical fuzzy systems, hybrid intelligent systems, and modeling of model partly known systems. For a function (system) with known hierarchical structure (i.e., one that can be represented as a composition of some simpler and lower dimensional subsystems), it is shown that hierarchical hybrid systems have the structure approximation capability in the sense that such a hybrid approximation scheme can approximate both the overall system and all the subsystems to any desired degree of accuracy. For a function (system) with unknown hierarchical structure, Kolmogorov's theorem is used to construct the hierarchical structure of the given function (system). It is then shown that hierarchical hybrid systems are universal approximators.     

两类层次模糊Mass-Assignment系统是全局逼近器

基于mass assignment 理论,提出了两类层次模糊mass assignment系统,并运用构造性证明过程证明了其全局逼近性质.由于类型1层次模糊系统的规则数与输入变量数呈线性关系,类型2层次模糊系统按逼近精度要求引入子模糊系统,因此,此两类层次模糊mass assignm ent系统可被用来有效地克服模糊规则爆炸问题,即所谓的规则数与输入变量数呈指数关系问题.     

Hierarchical multi-criteria risk-benefit analysis in fuzzy environment

The objectives of this paper are: (1) to utilize hierarchical fuzzy technique for order preference by similarity to ideal solution (TOPSIS) to evaluate the most suitable RFID-based systems decision and (2) to list key risks and benefits of radio frequency identification technology in library services. Researcher explains the importance of selection criteria for evaluation of RFID-based systems. It provides key elements on radio frequency identification, fuzzy hierarchical TOPSIS methodology and an algorithm that can be followed to solve the problem. A sample problem using the algorithm is solved and results are explained. Due to the fact that a better management of a library system is related to the full understanding of the technologies implemented and the system under consideration, some background on the radio frequency identification technology is provided and the kind of systems that most likely managements would face with and select are provided.     

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 sequential method for system identification in hierarchical structure

Implicit in all of hierarchical systems theory is the idea that it is generally easier to deal with several low order systems than with one system of high order. The basic idea of hierarchical systems theory is to decompose a large dimensional system into smaller dimensioned sub-systems in such a way that the overall system objectives can be met.

This paper is concerned with the application of hierarchical system theory to the identification problem. Specifically, the equations associated with a given identification problem are recast such that they may be decomposed into infimal subproblems of system identification which can be coordinated using hierarchical systems theory.

The maximum a posteriori approach to system identification is taken. This leads to a two point boundary value problem solution which determines optimum state and parameter estimates and estimates of any unknown prior statistics. Invariant imbedding is used to resolve this two point boundary value problem such that a recursive or sequential solution to the identification problem is obtained. Several examples indicate the use of the identification algorithms.     

复杂系统的递阶模糊辨识

针对Takagi_Sugeno模糊模型 (T_S模型 )严重的维数灾问题, 借鉴GMDH算法, 提出了一种新的复杂系统递阶模糊辨识方法. 本文首先详细描述了由两输入变量的特殊T_S模型所组成的递阶模糊模型 ;然后提出了具体的辨识该递阶模糊模型的方法. 该方法的特点是 :a)在结构辨识阶段, 用FCM模糊聚类方法评价系统中每个输入变量的重要性, 以便构造合理的递阶模糊模型 ;b)预先合理地确定了所要辨识的参数的初始值, 用扩展卡尔曼滤波方法可很快地得到这些参数. 最后, 给出的仿真实例说明了本文辨识方法的有