云映射和映射隶属云*

为描述事物间关系的不确定性及其变化情况,提出云映射概念。对定义域的每个元素,通过随机变量将其非确定地变换到可能的取值空间,各随机变量的分布特征在定义域上构成特征函数,能够反映非确定变换随自变量的变化情况;提出了映射的隶属云概念,云映射在定义域全体元素的隶属云片构成映射的隶属云;采用映射的期望(即精确函数)、熵函数和超熵函数描述定性概念在整个自变量取值空间的变化情况,给出了正向映射云和逆向映射云算法。以人类记忆的遗忘过程为例,说明了云映射和映射隶属云的有效性及其应用前景。     

正态云隶属度函数确定的FSM方法

隶属度函数及其确定方法的研究具有重要意义。采用正态云模型表示的隶属度函数综合了模糊性和随机性,具有普适性;提出了确定隶属度函数的模糊减法均值聚类(FSM)方法,得到了最优聚类中心和数据的隶属度。实例仿真表明,采用该方法确定了石油钻井中总体积的正态云隶属度函数,解决了隶属度函数难以客观描述和难以确定的问题。     

利用云模型实现FSVM遥感影像分类的隶属度算法

针对遥感影像分类面临的数据边界模糊性以及遥感信息解译过程不确定性的问题,结合模糊支持向量机在分类应用中可以有效避免噪声样本干扰的特点,提出一种基于云模型求解模糊支持向量机隶属度的方法。该方法通过无需隶属度的逆向云算法输入样本的定量位置得到样本类别的数字特征,再根据正向云算法计算得到每个样本对其定性类别的隶属度。实验结果表明,采用基于云模型隶属度的模糊支持向量机对遥感影像的分类方法是可行的,并能够有效提高对遥感影像的分类精度。     

云模型的隶属概念判定中阈值生成

在基于云模型的隶属概念判定算法中,人工给定的阈值不能根据对象隶属的多个概念的特征进行调整,从而影响到判定算法的适应性。基于云模型的“[3σ]规则”,提出一种自适应阈值生成算法。由其得到的阈值用于基于云模型的隶属概念判定算法,不仅使得原有的隶属概念判定算法可适用于不同特征的概念,而且使其更加符合人们的认识规律。阈值生成算法在不确定性的定性定量转换方面也具有较高的应用价值。     

基于隶属度理论的云服务行为信任评估模型研究

针对云用户难以在大量性能特征不同的云服务提供者中找到满足自己性能偏好和特定信任等级的云服务的问题,建立了一个合理的、科学的云服务行为信任评估系统。设计了云服务行为信任评估系统框架,基于隶属度理论建立了云服务行为信任评估模型,利用综合信任云重心评价法来计算云服务行为信任度,经过实验分析,该模型能够根据用户性能需求,对云服务进行更准确、科学的信任评估。     

基于云模型的隶属概念判定算法的改进

在人工智能领域中，李德毅教授等提出的定性定量不确定性转换模型——云模型，把概念的模糊性和随机性完全集成到一起，构成定性数据和定量数据的相互映射。但是，在利用云模型进行隶属概念的判定的算法中，不论对象是否明确属于某个概念，一律进行不确定性判定，过分地强调了模糊性和随机性。这不符合人类的认识规律，而且增加了算法的时间复杂度，甚至导致隶属概念判定的明显错误。该文根据人类认识规律对上述算法进行了改进。对那些可以明确确定属于某概念的对象，不再进行不确定性判定，直接被认定为属于该概念，只对处于多个概念边缘的不能确定属于某个概念的对象进行不确定性判定，使其符合人类的认识规律，降低了算法的时间复杂度。     

隶属函数的网络表达及其在声呐信号识别中的应用

根据神经网络具有高度非线性映射能力和并行计算能力，本文提出了一种用神经网络表达隶属函数的方法，得到的隶属函数可以并行计算隶属度，并能适应环境的变化；同时利用这种方法网络输出的隶属度以及模糊集合的代数运算，本文采用了多网络组合结构，应用到声呐回波信号识别中，与单网络结构相比，取得了较好的识别效果     

模糊控制中隶属函数的自动生成

本文摘要分析了模糊控制中模糊语言变量的隶属函数，提出了一种实用的隶属函数设计方法经对多种实例的设计，均获得满意的结果。     

基于云模型的隶属概念判定算法的改进

在人工智能领域中,李德毅教授等提出的定性定量不确定性转换模型——云模型,把概念的模糊性和随机性完全集成到一起,构成定性数据和定量数据的相互映射。但是,在利用云模型进行隶属概念的判定的算法中,不论对象是否明确属于某个概念,一律进行不确定性判定,过分地强调了模糊性和随机性。这不符合人类的认识规律,而且增加了算法的时间复杂度,甚至导致隶属概念判定的明显错误。该文根据人类认识规律对上述算法进行了改进。对那些可以明确确定属于某概念的对象,不再进行不确定性判定,直接被认定为属于该概念,只对处于多个概念边缘的不能确定属于某个概念的对象进行不确定性判定,使其符合人类的认识规律,降低了算法的时间复杂度。     

赋工序完工隶属函数的网络计划模型

文中为处理网络计划模型中工序作业时间的不确定性,提出了用工序完工隶属函数描述作业时间不确定性,并给出了求工程的完工隶属函数的方法,最后说明了利用工程的完工隶属函数进行关键路线分析。     

MEMBERSHIP IN A COMPOUND FUZZY SUBSET

Abstract

We first provide a new formulation for a fuzzy subset as a joint relation of the variables, the element and the membership grade of the element. This relationship is developed by appreciating the fact that a fuzzy subset, as is any set, is a union of the elements which constitute it. With a compound fuzzy subset of X defined as a fuzzy subset defined over a base set whose elements are fuzzy subsets of X we suggest a method for obtaining the membership grade of the elements of X in this compound fuzzy subset. This method uses the formulation suggested at the beginning.     

MEMBERSHIP FUNCTIONS SHAPE AND ITS INFLUENCE ON THE DYNAMICAL BEHAVIOUR OF FUZZY LOGIC CONTROLLER

In the present paper, the influence of membership functions shape on the fuzzy logic controller output surface is investigated and discussed. Bell-shaped membership functions with two parameters are used. An example with linear object under control is shown. The results are presented graphically and can serve to determine two parameters with respect to the desired action of fuzzy controller.     

一种基于模糊聚类的隶属函数定义方法

隶属函数的确定是模糊集合理论及其应用的基本而关键的问题。本文提出了一种基于模糊聚类的、以训练样本数据为依据的、自动地确定模糊集合隶属函数的方法，为开发模糊系统节省了大量的时间和精力。     

AUTOMATICALLY CONSTRUCTING MEMBERSHIP FUNCTIONS AND GENERATING FUZZY RULES USING GENETIC ALGORITHMS

The most important task in designing a fuzzy classification system is to find a set of fuzzy rules from training data to deal with a specific classification problem. In recent years, many methods have been proposed to construct membership functions and generate fuzzy rules from training data for handling fuzzy classification problems. We propose a new method to generate fuzzy rules from training data by using genetic algorithms (GAs). First, we divide the training data into several clusters by using the weighted distance clustering method and generate a fuzzy rule for each cluster. Then, we use GAs to tune the membership functions of the generated fuzzy rules. The proposed method attains a higher average classification accuracy rate than the existing methods.     

一种基于云模式连续型属性离散化的算法

在数据挖掘研究过程中，对连续型属性一般要进行离散化。特别是在模糊数据挖掘中，还要对离散化的区间进行模糊处理。文中依托云模式，并结合粗糙集理论提出一种新的连续型属性离散化算法。     

Type‐1 OWA Unbalanced Fuzzy Linguistic Aggregation Methodology: Application to Eurobonds Credit Risk Evaluation

In decision making, a widely used methodology to manage unbalanced fuzzy linguistic information is the linguistic hierarchy (LH), which relies on a linguistic symbolic computational model based on ordinal 2‐tuple linguistic representation. However, the ordinal 2‐tuple linguistic approach does not exploit all advantages of Zadeh's fuzzy linguistic approach to model uncertainty because the membership function shapes are ignored. Furthermore, the LH methodology is an indirect approach that relies on the uniform distribution of symmetric linguistic assessments. These drawbacks are overcome by applying a fuzzy methodology based on the implementation of the type‐1 ordered weighted average (T1OWA) operator. The T1OWA operator is not a symbolic operator and it allows to directly aggregate membership functions, which in practice means that the T1OWA methodology is suitable for both balanced and unbalanced linguistic contexts and with heterogeneous membership functions. Furthermore, the final output of the T1OWA methodology is always fuzzy and defined in the same domain of the original unbalanced fuzzy linguistic labels, which facilitates its interpretation via a visual joint representation. A case study is presented where the T1OWA operator methodology is used to assess the creditworthiness of European bonds based on real credit risk ratings of individual Eurozone member states modeled as unbalanced fuzzy linguistic labels.     

图象隶属度及其在人脸识别中的应用

文中首先从代数理论和模糊数学出发，讨论向量空间中任一子空间对任一向量的接纳程度，将其定义为向量隶属度，并证明它具有一些不变性，然后将它推广应用于图象识别中，构造图象隶属度，人脸识别实验结果表明，图象隶属度具有良好的识别分离能力。     

MEMBERSHIP FUNCTIONS SHAPE AND ITS INFLUENCE ON THE STABILITY OF FUZZY CONTROL SYSTEMS

In the present paper the investigation of the influence of nonlinearities in membership functions shape on stability of the system linear object-nonlinear fuzzy logic controller is carried out by means of the second Lyapunov's method. The extension of the circle stability criterion for the transformed in the space of error and its derivative system is derived. Simulation investigations with a simple linear object that prove the obtained theoretical results are carried out.     

Genetic tuning of fuzzy inference within fuzzy classifier systems

Abstract: In generating a suitable fuzzy classifier system, significant effort is often placed on the determination and the fine tuning of the fuzzy sets. However, in such systems little thought is given to the way in which membership functions are combined within the fuzzy rules. Often traditional fuzzy inference strategies are used which consequently provide no control over how strongly or weakly the inference is applied within these rules. Furthermore such strategies will allow no interaction between grades of membership. A number of theoretical fuzzy inference operators have been proposed for both regression and classification problems but they have not been investigated in the context of real-world applications. In this paper we propose a novel genetic algorithm framework for optimizing the strength of fuzzy inference operators concurrently with the tuning of membership functions for a given fuzzy classifier system. Each fuzzy system is generated using two well-established decision tree algorithms: C4.5 and CHAID. This will enable both classification and regression problems to be addressed within the framework. Each solution generated by the genetic algorithm will produce a set of fuzzy membership functions and also determine how strongly the inference will be applied within each fuzzy rule. We investigate several theoretical proven fuzzy inference techniques (T-norms) in the context of both classification and regression problems. The methodology proposed is applied to a number of real-world data sets in order to determine the effects of the simultaneous tuning of membership functions and inference parameters on the accuracy and robustness of fuzzy classifiers.     

A design methodology for fuzzy system interfaces

Conceptually, a fuzzy system interacting with a numerical environment has three components: a numeric/linguistic interface, a linguistic processing unit, and a linguistic/numeric interface. At these interfaces, membership functions representing linguistic terms play a top role both for the linguistic meaning provided and for the pre/post information processing introduced to the fuzzy system. Considering these issues, a set of membership function properties is postulated. Furthermore, an expert-free interface design methodology able to meet these properties, and based on the concept of optimal interfaces, is proposed. This concept simply states an equivalence between information format (numeric and linguistic), thereby making the methodology appealing from the applicational point of view. An algorithm is developed, and brief notes on selected applications are outlined stressing relevant issues of the proposed methodology