模糊概率神经网络水质评价模型及其应用

鉴于水质类型和分级标准存在模糊性,将模糊数学中的相对隶属度理论和概率神经网络和相结合,构建了模糊概率神经网络水质评价模型(FPNN).阐明了该模型的构建方法,提出了基于指标相对隶属度矩阵插值构建学习样本的方法,并将该模型应用于实际水质评价.通过与综合评判法、属性识别法和BP网络法的比较,验证了该模型操作简便,评价结果客观可靠.     

用模糊集合描述模糊信息的无效性

用模糊集合描述模糊信息无效的原因是,把原本是论域与状态空间上二元函数的模糊隶属函数看成是论域上的一元函数,用模糊集合描述的模糊信息,不能支持模糊集合转换;使得通过模糊集合转换处理模糊信息的模糊数学,不得不借用不是数学计算、无缘数学模型的"取大取小"实现模糊集合转换;结果是背离数学计算的模糊数学,不能为处理模糊信息提供算法支持,导致大量需要处理的模糊信息滞留至今.还原模糊信息是高维状态空间上分类数据的真实面目,把处理模糊信息明确为由指标隶属度确定目标隶属度的隶属度转换,是模糊数学回归数学的唯一正确途径.     

多对象多指标多级别模糊模式识别模型的构建

给出对象指标相对隶属度矩阵和标准指标值相对隶属度矩阵的建立方法;提出如何构建一种新的模糊模式识别模型.     

基于AFS拓扑和AFCM的模糊聚类分析

在分析AFS方法和AFCM算法的基础上,设计了一个新的模糊聚类算法.它首先应用AFS拓扑理论计算得到数据的相对距离,然后将相对距离应用于改进后的AFCM算法中,并进行了聚类实验.实验结果证明这样的聚类算法优于传统的HCM、FCM聚类算法,而且该方法能应用于含有布尔值或模糊概念的聚类分析中.     

一个新的模糊聚类有效性指标

提出了一个判别模糊聚类中聚类数有效性的新指标.首先利用FCM算法对数据集进行模糊聚类,通过隶属度矩阵和聚类中心构建加权二分网络.然后通过改进加权二分网络的模函数,定义一个新的聚类有效性指标.为了检验该有效性指标的性能,选取了三个常见的有效性指标在十五个数据集上进行了对比.实验结果表明,该有效性指标具有较好的性能.     

基于混合型模糊聚类分析的降水区域分类法

在混合型模糊聚类分析的基础上,先用传递闭包法得出动态聚类结果,然后引用F统计量找到最佳分类,针对此最佳分类给出具体算法求得初始分类矩阵,然后利用模糊C-均值算法对初始分类矩阵进行迭代计算,对原分类结果进行软划分修正从而得出最终聚类结果.方法减少了两次人为因素对聚类结果的干扰.将其应用于降水区域划分的实证分析表明,可以对降水区域进行更为有效的划分.     

区间模糊ISODATA动态聚类算法

目前模糊技术已经应用于许多智能系统,如模糊关系与模糊聚类.聚类是数据挖掘的重要任务,它将数据对像分成多个聚类,在同一个聚类中,对象的属性特征之间具有较高的相似度,有很大研究及应用价值.结合数据库中的挖掘技术,对属性特征为区间数的多属性决策问题,提出了一种基于区间数隶属度的区间模糊ISODATA动态聚类方法.     

基于随机采样模糊聚类和卡尔曼滤波方法的模糊辨识

提出一种新的基于模糊聚类和卡尔曼滤波方法的模糊辨识算法 .该方法是基于快速模糊聚类 ,计算给定样本在各类中的隶属度 ,并利用卡尔曼滤波方法辨识模糊模型的结论参数 .整个辨识过程与一般的模糊聚类方法 [1 ]相比 ,需要的 CPU时间大大缩短 .最后通过仿真实例验证了该方法的有效性 .     

土壤分类的模糊集成算法与应用

土壤是一个多性状的连续体,其分类的首选方法是模糊聚类分析.但是模糊聚类分析中现有的基于模糊等价关系的动态聚类法和模糊c-均值法各有利弊,采用其中一种方法聚类肯定存在不足.为此集成两种聚类方法的优点,避其缺点,提出了用基于模糊等价关系的动态聚类方法和方差分析方法确定聚类数目和初始聚类中心,再用模糊c-均值法决定最终分类结果的集成算法,并将其应用到松花江流域土壤分类中,得到了较为切合实际的分类结果.     

直觉模糊矩阵幂序列的收敛准则

首先,给出直觉模糊矩阵幂的隶属度和非隶属度的表达形式.其次,定义直觉模糊矩阵的最小正周期数和收敛指数,得到单增的直觉模糊矩阵幂序列是收敛的结论.最后,给出直觉模糊矩阵幂序列收敛的两个充分条件.     

Type-2 T–S fuzzy impulsive control of nonlinear systems

A novel impulsive control approach based on interval Type-2 T–S fuzzy model has been presented for nonlinear systems in this paper. This approach makes up for the drawback of Type-1 fuzzy impulsive control, which cannot fully handle the uncertainties in describing the complex nonlinear systems by Type-1 fuzzy membership functions and cannot give rigorous fuzzy rules. Further more, this approach uses the “broad band” effect of the Type-2 membership functions to solve the noise of training data and exterior disturbance of the Type-1 fuzzy impulsive control. By using Lyapunov theory and Lipschitz condition, which is combined with integrated approaches such as comparison methods and linear matrix inequalities, the Type-2 fuzzy impulsive controller is designed and the general asymptotical stability analysis of the systems is given. Finally, the simulation of the inverted pendulum model demonstrates the validity and superiority of the proposed method by easily determining the membership functions and choosing minimum number of fuzzy rules and the method can handle random disturbance and data uncertainties very well.     

Membership maximization prioritization methods for fuzzy analytic hierarchy process

Fuzzy analytic hierarchy process (FAHP) has increasingly been applied in many areas. Extent analysis method is the popular tool for prioritization in FAHP, although significant technical errors are identified in this study. With addressing the errors, this research proposes membership maximization prioritization methods (MMPMs) using different membership functions as the novel solutions. As a lack of research about effectiveness measurement on the crisp/fuzzy prioritization methods, this study proposes membership fitness index to evaluate the effectiveness of the prioritization methods. Comparisons with the other popular fuzzy/crisp prioritization methods including modified fuzzy preference programming, Direct least squares, and Eigen value are conducted and analyses indicate that MMPMs lead to much more reliable result in view of membership fitness index. A numerical example demonstrates the usability of MMPMs for FAHP, and thus MMPMs can effectively be applied to various decision analysis applications.     

The extended linear assignment method for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets

The theory of interval-valued intuitionistic fuzzy sets is useful and beneficial for handling uncertainty and imprecision in multiple criteria decision analysis. In addition, the theory allows for convenient quantification of the equivocal nature of human subjective assessments. In this paper, by extending the traditional linear assignment method, we propose a useful method for solving multiple criteria evaluation problems in the interval-valued intuitionistic fuzzy context. A ranking procedure consisting of score functions, accuracy functions, membership uncertainty indices, and hesitation uncertainty indices is presented to determine a criterion-wise preference of the alternatives. An extended linear assignment model is then constructed using a modified weighted-rank frequency matrix to determine the priority order of various alternatives. The feasibility and applicability of the proposed method are illustrated with a multiple criteria decision-making problem involving the selection of a bridge construction method. Additionally, a comparative analysis with other methods, including the approach with weighted aggregation operators, the closeness coefficient-based method, and the auxiliary nonlinear programming models, has been conducted for solving the investment company selection problem to validate the effectiveness of the extended linear assignment method.     

小波分析与模糊系统分析的联系

讨论小波基函数与模糊集隶属函数之间的联系 ,证明模糊系统研究与应用中的隶属函数都可以由称之为简单小波的母函数表出 ,反之每一简单小波也可以由某一隶属函数表出 ,从而验证简单小波类与某一隶属函数类的一一对应关系。该结果进一步揭示模糊推理和模糊控制的实质 ,为在模糊系统辨识、模糊控制和模糊数据分析等诸多领域充分利用近代小波分析的成果提供新思路     

基于Fuzzy理论的一种医疗诊断模型

首先从大量文献中整理出不同经脉中穴位主治病症的个数及穴位在文献中出现的频数等数据,并对现有的模糊聚类分析方法进行了研究,依据改进后的FCM法对手少阳三焦经上的全部穴位按重要程度进行了分类.同时通过病症现象与穴位之间的隶属关系,提出由历史数据及专家优序数综合确定模糊隶属度的方法,建立模糊医疗诊断模型.该模型为利用经络中的穴位快速、准确治疗疾病提供了理论方法.     

A simple approach to fuzzy critical path analysis in project networks

This paper develops a simple approach to critical path analysis in a project network with activity times being fuzzy numbers. The idea is based on the linear programming (LP) formulation and fuzzy number ranking method. The fuzzy critical path problem is formulated as an LP model with fuzzy coefficients of the objective function, and then on the basis of properties of linearity and additivity, the Yager’s ranking method is adopted to transform the fuzzy LP formulation to the crisp one which can be solved by using the conventional streamlined solution methods. Consequently, the critical path and total duration time can be obtained from the derived optimal solution. Moreover, in this paper we also define the most critical path and the relative path degree of criticality, which are theoretically sound and easy to use in practice. An example discussed in some previous studies illustrates that the proposed approach is able to find the most critical path, which is proved to be the same as that derived from an exhausted comparison of all possible paths. The proposed approach is very simple to apply, and it is not require knowing the explicit form of the membership functions of the fuzzy activity times.     

Exponential family mixed membership models for soft clustering of multivariate data

For several years, model-based clustering methods have successfully tackled many of the challenges presented by data-analysts. However, as the scope of data analysis has evolved, some problems may be beyond the standard mixture model framework. One such problem is when observations in a dataset come from overlapping clusters, whereby different clusters will possess similar parameters for multiple variables. In this setting, mixed membership models, a soft clustering approach whereby observations are not restricted to single cluster membership, have proved to be an effective tool. In this paper, a method for fitting mixed membership models to data generated by a member of an exponential family is outlined. The method is applied to count data obtained from an ultra running competition, and compared with a standard mixture model approach.     

基于模糊中值滤波的椒盐噪声去除方法

研究基于模糊中值滤波的椒盐噪声去除方法。通过比较图像各像素点的灰度值,定义基于图像梯度信息的各点被判别为噪声点的模糊隶属函数。利用此模糊隶属函数对中值滤波方法进行加权,得到了一种加权中值滤波器,可实现边缘处椒盐噪声的有效滤除。讨论这种模糊加权方法与其它先进滤波方法的结合途径,指出了其推广应用价值。最后利用数值实验验证本文方法的有效性,结果表明,相比于自适应中值滤波方法,本文方法得到的滤波图像在峰值信噪比及结构相似度方面均有明显提高。     

Exact analytical inversion of TSK fuzzy systems with singleton and linear consequents

In literature, exact inversion methods for TSK fuzzy systems exist only for the systems with singleton consequents. These methods have binding limitations such as strong triangular partitioning, monotonic rule bases and/or invertibility check. These extra limitations lessen the modeling capabilities of the TSK fuzzy systems. In this study, an exact analytical inversion method for TSK fuzzy systems with singleton and linear consequents is presented. The only limitation of the proposed method is that the inversion variable should be represented by piecewise linear membership functions (PWL-MFs). In this case, the universe of discourse of the inversion variable is divided into specific regions in which only one linear piece exists for each PWL-MF at most. In the proposed method, the analytical formulation of TSK fuzzy system is expressed in terms of the inversion variable by using linear equations of PWL-MFs. Thus, the fuzzy system output in any region can be obtained by using the appropriate parameters of the linear equations of PWL-MFs defined within the related region. This expression provides a way to obtain linear and quadratic equations in terms of the inversion variable for TSK fuzzy systems with singleton and linear consequents, respectively. So, it becomes very easy to find exact inverse solutions for each region by using explicit analytical solutions for linear or quadratic equations. The proposed inversion method has been illustrated through simulation examples.