模糊树模型及其在复杂系统辨识中的应用

基于二叉树和模糊逻辑理论,提出了一种用于复杂系统建模的模糊树模型.将线性 模型和模糊集组织在树结构上,并给出了更新线性模型系数和模糊集隶属度函数的混合算 法.与其他建模方法相比,如ANFIS,模糊树模型计算量小,精度高,尤其在高维数据建模中 更为明显.仿真结果描述了这种方法的性能.     

考虑重要输入变量选择的非线性系统模糊辨识

针对有数百个可能输入的复杂非线性动态系统模糊建模问题,本文提出一种新的考虑重要输入变量选择的模糊辨识方法.首先采用两阶段模糊曲线方法(TSFC)从大量可选择的输入变量中给出各输入变量与输出之间的关联度权重,根据输入变量指标快速选择出重要的输入变量,然后采用模糊聚类(FCM)和高斯(Gaussian)型隶属函数确定模糊模型前提参数,采用递推最小二乘(RLS)辨识出模糊模型结论参数.最后通过对Mackey-Glass混沌时间序列和Box-Jenkins煤气炉数据两个国际标准例题模糊建模验证了该方法的有效性,并将该方法应用到一个实际气动变载荷加载系统的模糊建模中,验证了该方法的实用性.     

基于混合聚类算法的模糊函数系统辨识方法

针对传统模糊系统存在的结构难以确定和参数辨识复杂的问题,提出了一种基于混合聚类算法的模糊函数系统辨识算法.与一般的模糊函数系统相比,混合聚类算法结合模糊C均值和模糊C回归模型聚类算法的样本距离.在模型预测部分,采用高斯函数计算每个输入变量的隶属度,利用输入变量隶属度的模糊化算子得到输入向量的隶属度.应用于Box-Jenkins煤气炉数据、一个双入单出的非线性系统和Mackey-Glass混沌时间序列数据的试验结果表明,本文算法具有很好的辨识效果,从而验证了本文算法的有效性与实用性.     

基于密度聚类的神经模糊系统建模算法

神经模糊系统经常被用来对非线性系统建模,并能取得很好的效果.以往的模糊系统建模方法存在着输入空间划分个数难以确定和规则冗余的问题,这些问题阻碍了模糊系统的应用.基于动态阈值DENCLUE和相似规则合并的神经模糊系统建模算法DDTSRM(DENCLUE using a dynamic threshold and similar rules merging),首先在DENCLUE算法中使用动态阈值来合并密度吸引子,得到DDT算法.DDTSRM利用DDT算法不依赖初始参数的特点,解决了输入空间划分个数难以确定的问题.因为DDT算法可以得到任意形状和任意密度的聚类结果的特性,所以提高了模糊系统模型的准确性.辨识出模型的初始结构后,DDTSRM通过计算模糊集合之间的相似度来减少规则冗余,使模糊系统模型结构得到优化.最后利用BP算法对系统模型进行训练,进而提高系统的建模精度.以S-Y模糊系统模型为原型,在两输入一输出的非线性函数和Box-Jenkins数据上的仿真实验证明了DDTSRM算法在神经模糊系统建模应用的有效性,能够取得精确的建模效果.     

基于直觉模糊可能性分布的三支决策模型的研究

直觉模糊集理论和可能性理论的融合是不确定问题领域的一个研究热点。文中提出了一种基于直觉模糊可能性分布的直觉模糊可能性测度(Intuitionistic Fuzzy Probability Measurement,IFPM),并在此基础上构建了三支决策模型。首先,定义了直觉模糊决策空间及该空间上的直觉模糊可能性分布,并对其性质进行了证明,给出了论域对象的隶属度和非隶属度可能性均值的计算方法。然后,讨论了论域对象的隶属度和非隶属度可能性均值与决策阈值的关系,分析了它们之间的概率分布情况。根据概率分布－可能性分布的转换关系,给出决策规则和三支决策模型,提出了一种基于直觉模糊可能性分布的IFPM决策风险计算方法。最后,考虑论域中对象的增减变化引起的IFPM变化,给出对应公式并对动态决策过程进行分析,同时通过实例验证了该模型的有效性。     

基于子集融合与规则简约的磨矿过程模糊建模

针对选矿厂磨矿生产过程的模糊建模问题,本文提出一种基于模糊集融合和规则简约的模糊建模方法.该方法针对基于数据建立的磨矿过程Takagi-Sugeno模型,采用模糊C均值聚类方法对同一变量下的隶属度函数参数进行聚类,得到对不同工况具有代表性的融合后的隶属度函数,来降低过度拟合的影响.此外,本文根据规则库中的规则权值,对前件相同的冗余规则进行约简,形成最终的离线模糊规则库,有效提高了规则库的泛化能力.为验证本文方法的有效性,分别采用经典数据与实际工业数据进行了实验论证,从精度和泛化能力上体现了本文方法的优势.     

基于遗传算法的模糊控制器的优化设计——采用模糊数据挖掘技术

论文为模糊系统建模提出了一种新颖的方法——由输入输出数据集合设计基于遗传算法的模糊控制器,该方法采用模糊数据挖掘技术,从大量的输入输出数据集合中自动地提取模糊规则模型,确定模糊分割点及各变量的隶属度函数;并利用实数编码的遗传算法RGA对隶属度函数参数进行全面优化。最后通过实例及仿真验证了该方法的有效性。     

基于公理化模糊集合的模糊推理方法

以公理化模糊集合理论作为基础,把模糊推理看成两个模糊隶属空间之间的映射,利用输入模糊集合在模糊隶属空间中的构成方式,给出了模糊推理输出结果的3种基本形式.对于强否定算子、t-模算子、t-余模算子,利用Minkowski积分形式的距离讨论了这些算子在模糊隶属空间中的扰动性,并在此基础之上分析所提模糊推理方法的连续性.     

BP算法改进及在控制系统中应用

研究控制问题,为了解决系统的稳定性和系统的精度,采用模糊控制方法,对模糊隶属度函数输入域上致密分布的要求,采用隶属函数约束寻优对基于BP算法的模糊神经网络进行了改进。算法首先采用-S函数对输入变量进行非线性映射,函数在把输入变量映射人确定区域的同时最大程度上保留了原样本的信息,然后根据经验知识给出隶属函数参数的优化范围,保证了模糊变量在输入域上的致密分布。经过仿真实验,仿真结果取得了与理论分析一致的实验结果,保证系统的稳定性。     

模糊模型的结构辨识

一、问题的描述考虑MISO模糊系统y(t)=x_1(t)ox_2(t)o…ox_n(t)oR,(1)其中y(·)为输出模糊变量;x(·)为输入模糊变量;R为基于参考模糊集合的模糊关系;“o”为基于参考模糊集合的合成算子;n为输入模糊变量的个数.模糊模型的辨识就是确定各模糊变量x_i(·),y(·)在其论域上参考模糊集合的隶属函数(即结构)和模糊关系     

一种基于粒子群算法的模糊隶属函数优化方法

在分析图像模糊增强算法对于隶属函数及其模糊区域选择方法不足的基础上,提出一种新的基于粒子群算法的模糊隶属函数优化方法。该方法给出一个新模糊熵的定义,这个新模糊熵定义不仅考虑到图像在模糊域中划分区域时随隶属函数变化而变化的情况,同时又考虑到图像在空域中划分区域时随隶属函数变化而变化的情况。这样就使得图像依照最大熵准则变换到模糊域更能够有效地反映图像的固有信息。另外,根据图像增强算法中使用double型数据类型的特点,采用改进粒子群优化算法寻求隶属函数的最优参数。将新算法应用于图像增强中,取得了优于现有大多数模糊增强算法的效果。     

A Three-Dimensional Fuzzy Control Methodology for a Class of Distributed Parameter Systems

The traditional fuzzy set is two-dimensional (2-D) with one dimension for the universe of discourse of the variable and the other for its membership degree. This 2-D fuzzy set is not able to handle the spatial information. The traditional fuzzy logic controller (FLC) developed from this 2-D fuzzy set should not be able to control the distributed parameter system that has the tempo-spatial nature. A three-dimensional (3-D) fuzzy set is defined to be made of a traditional fuzzy set and an extra dimension for spatial information. Based on concept of the 3-D fuzzy set, a new fuzzy control methodology is proposed to control the distributed parameter system. Similar to the traditional FLC, it still consists of fuzzification, rule inference, and defuzzification operations. Different to the traditional FLC, it uses multiple sensors to provide 3-D fuzzy inputs and possesses the inference mechanism with 3-D nature that can fuse these inputs into a so called ldquospatial membership function.rdquo Thus, a simple 2-D rule base can still be used for two obvious advantages. One is that rules will not increase as sensors increase for the spatial measurement; the other is that computation of this 3-D fuzzy inference can be significantly reduced for real world applications. Using only a few more sensors, the proposed FLC is able to process the distributed parameter system with little complexity increased from the traditional FLC. The 3-D FLC is successfully applied to a catalytic packed-bed reactor and compared with the traditional FLC. The results demonstrate its effectiveness to the nonlinear unknown distributed parameter process and its potential to a wide range of engineering applications.     

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.     

Structure identification in complete rule-based fuzzy systems

The identification of a model is one of the key issues in the field of fuzzy system modeling and function approximation theory. There are numerous approaches to the issue of parameter optimization within a fixed fuzzy system structure but no reliable method to obtain the optimal topology of the fuzzy system from a set of input-output data. This paper presents a reliable method to obtain the structure of a complete rule-based fuzzy system for a specific approximation accuracy of the training data, i.e., it can decide which input variables must be taken into account in the fuzzy system and how many membership functions (MFs) are needed in every selected input variable in order to reach the approximation target with the minimum number of parameters     

Development of a systematic methodology of fuzzy logic modeling

This paper proposes a systematic methodology of fuzzy logic modeling for complex system modeling. It has a unified parameterized reasoning formulation, an improved fuzzy clustering algorithm, and an efficient strategy of selecting significant system inputs and their membership functions. The reasoning mechanism introduces 4 parameters whose variation provides a continuous range of inference operation. As a result, we are no longer restricted to standard extremes in any step of reasoning. The fuzzy model itself can then adjust the reasoning process by optimizing the inference parameters based on input-output data. The fuzzy rules are generated through fuzzy c-means (FCM) clustering. Major bottlenecks are addressed and analytical solutions are suggested. We also address the classification process to extend the derived fuzzy partition to the entire output space. In order to select suitable input variables among a finite number of candidates (unlike traditional approaches) we suggest a new strategy through which dominant input parameters are assigned in one step and no iteration process is required. Furthermore, a clustering technique called fuzzy fine clustering is introduced to assign the input membership functions. In order to evaluate the proposed methodology, two examples-a nonlinear function and a gas furnace dynamic procedure-are investigated in detail. The significant improvement of the model is concluded compared to other fuzzy modeling approaches     

A Novel Method of Ranking Hesitant Fuzzy Values for Multiple Attribute Decision‐Making Problems

Despite of several generalizations of fuzzy set theory, the notion of hesitant fuzzy set (HFS), which permits the membership having a set of possible values, is interesting and very useful in modeling real‐life problems with anonymity. In this article, we introduce a new score function for ranking hesitant fuzzy elements (HFEs), which are the fundamental units of HFSs. Comparison with the existing score function shows that the proposed method meets all the well‐known properties of a ranking measure and has no counterintuitive examples. On the basis of the relationships between the aggregation operators for HFEs, we derive a series of interesting properties of the new score function. Finally, we apply the proposed score function to solve the hesitant fuzzy multiattribute decision‐making problems.     

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。     

基于空间模糊纹理光谱的多光谱遥感图像分类方法

为了充分利用各波段的纹理信息，针对遥感图像不同波段之间具有较大相关性的特点，提出了一种用空间模糊纹理光谱描述多光谱遥感图像纹理特征的方法。根据纹理特征具有多尺度的特性，对原始图像进行二次模糊纹理滤波，一次滤波采用平面三角隶属度函数，二次滤波采用空阃距离代替平面距离形成滤波隶属度函数，其模糊滤波图像的隶属度分布称之为空间模糊纹理光谱。用FasART神经网络分类验证，实验结果表明，该方法具有较高的分类精度，尤其对纹理特征较为复杂的区域的分类效果更为明显。     

Fuzzy functions based ARX model and new fuzzy basis function models for nonlinear system identification

In this study, auto regressive with exogenous input (ARX) modeling is improved with fuzzy functions concept (FF-ARX). Fuzzy function with least squares estimation (FF-LSE) method has been recently developed and widely used with a small improvement with respect to least squares estimation method (LSE). FF-LSE is structured with only inputs and their membership values. This proposed model aims to increase the capability of the FF-LSE by widening the regression matrix with lagged input–output values. In addition, by using same idea, we proposed also two new fuzzy basis function models. In the first, basis of the fuzzy system and lagged input–output values are structured together in the regression matrix and named as “L-FBF”. Secondly, instead of using basis function, the membership values of the lagged input–output values are used in the regression matrix by using Gaussian membership functions, called “M-FBF”. Therefore, the power of the fuzzy basis function is also enhanced. For the corresponding models, antecedent part parameters for the input vectors are determined with fuzzy c-means (FCM) clustering algorithm. The consequent parameters of the all models are estimated with the LSE. The proposed models are utilized and compared for the identification of nonlinear benchmark problems.