FUZZY MEASURES AND FUZZY INTEGRALS: AN OVERVIEW

This paper provides an overview of fuzzy measures, fuzzy integration theories and Choquet's capacity theory. Belief, plausibility, and possibility measures are characterized as Choquet capacities and as fuzzy measures. The relationship between possibility measures, fuzzy sets, and approximate reasoning is established. Recent results on extensions of fuzzy measures, structural characteristics of fuzzy measures, and convergence of function sequences on fuzzy measure spaces are presented. Fuzzy measure integration concepts due to Sugeno and Choquet and their applications are discussed. An extensive list of references to the literature of fuzzy measures, Sugeno and Choquet integrals, fuzzy probabilities, fuzzy random variables, probabilistic sets, and random sets is provided. Applicalions discussed or referenced include information fusion, information retrieval, approximate reasoning, artificial intelligence, uncertainty theory, and control and decision theory.     

Precise wavelet for current signature in 3 IM

Induction motors, which are used worldwide as the “workhorse” in industrial applications, are intermittently subjected to faults, mainly the stator faults. In this paper, fault diagnostics of induction motor using current signature analysis, with wavelet transform, is treated as a pattern classification problem. The major steps in pattern classification are feature extraction, feature selection and classification. The feature extraction is done by wavelet transforms, using different wavelets which allow the use of long time intervals where there is precise low-frequency information, and shorter regions where there is precise high-frequency information. The extracted features are classified using the new generation pattern classification technique of Support Vector Machine (SVM) identification. Then the relative capability of the different wavelets, in performing the stator winding fault identification is analyzed and the best wavelet is selected.     

基于条件概率的粗糙集不确定性度量

通过语义分析,提出一种修正的粗糙集不确定性度量公理化定义。首先,对该定义的数学特征进行分析,提出两种基于条件概率的粗糙集不确定性度量方法;然后,证明它们满足所提出的公理化定义,并导出相应的知识不确定性度量,发现其中一个是现有条件信息熵,另一个与确定性度量形成互补关系。设计算例对各种不确定性度量进行比较分析,验证了所提出的度量公式与不确定性语义保持一致。     

Evaluation of soft possibilistic classifications with non-specificity uncertainty measures

The aim of this paper was to investigate the usefulness of non-specificity uncertainty measures to evaluate soft classifications of remote sensing images. In particular, we analysed whether these measures could be used to identify the difficulties found by the classifier and to estimate the classification accuracy. Two non-specificity uncertainty measures were considered, the non-specificity measure (NSp) and the U-uncertainty measure, and their behaviour was analysed to evaluate which is the most appropriate for this application. To overcome the fact that these two measures have different ranges, a normalized version (U_n) of the U-uncertainty measure was used. Both measures were applied to evaluate the uncertainty of a soft classification of a very high spatial resolution multispectral satellite image, performed with an object-oriented image analysis based on a fuzzy classification. The classification accuracy was evaluated using an error matrix and the user's and producer's accuracies were computed. Two uncertainty indexes are proposed for each measure, and the correlation between the information given by them and the user's and producer's accuracies was determined to assess the relationship and compatibility of both sources of information. The results show that there is a positive correlation between the information given by the uncertainty and accuracy indexes, but mainly between the uncertainty indexes and the user's accuracy, where the correlation achieved 77%. This study shows that uncertainty indexes may be used, along with the possibility distributions, as indicators of the classification performance, and may therefore be very useful tools.     

一种多传感器信息融合的可能性关联方法

由于传感器测量数据的不确定性,导致传统的关联方法关联正确率不高。引入可能性理论来表述测量数据的不确定性,很好地反映测量值与目标真值的相容程度,并建立了一种基于可能性分布的关联模型,将测量值与目标在特征分量上的统计距离进行模糊化,构造测量值关于目标的可能性分布,并量化二者之间的模糊关系,使关联问题转化为一种多目标决策问题。仿真实验验证了方法的有效性。     

Fuzzy XML data modeling with the UML and relational data models

Information imprecision and uncertainty exist in many real-world applications and for this reason fuzzy data modeling has been extensively investigated in various data models. Currently, huge amounts of electronic data are available on the Internet, and XML has been the de facto standard of information representation and exchange over the Web. This paper focuses on fuzzy XML data modeling, which is mainly involved in the representation model of the fuzzy XML, its conceptual design, and its storage in databases. Based on “possibility distribution theory”, we developed this fuzzy XML data model. We developed this fuzzy UML data model to design the fuzzy XML model conceptually. We investigated the formal conversions from the fuzzy UML model to the fuzzy XML model and the formal mapping from the fuzzy XML model to the fuzzy relational databases.     

Uncertainty Estimation Using Fuzzy Measures for Multiclass Classification

Uncertainty arises in classification problems when the input pattern is not perfect or measurement error is unavoidable. In many applications, it would be beneficial to obtain an estimate of the uncertainty associated with a new observation and its membership within a particular class. Although statistical classification techniques base decision boundaries according to the probability distributions of the patterns belonging to each class, they are poor at supplying uncertainty information for new observations. Previous research has documented a multiarchitecture, monotonic function neural network model for the representation of uncertainty associated with a new observation for two-class classification. This paper proposes a modification to the monotonic function model to estimate the uncertainty associated with a new observation for multiclass classification. The model, therefore, overcomes a limitation of traditional classifiers that base decisions on sharp classification boundaries. As such, it is believed that this method will have advantages for applications such as biometric recognition in which the estimation of classification uncertainty is an important issue. This approach is based on the transformation of the input pattern vector relative to each classification class. Separate, monotonic, single-output neural networks are then used to represent the "degree-of-similarity" between each input pattern vector and each class. An algorithm for the implementation of this approach is proposed and tested with publicly available face-recognition data sets. The results indicate that the suggested approach provides similar classification performance to conventional principle component analysis (PCA) and linear discriminant analysis (LDA) techniques for multiclass pattern recognition problems as well as providing uncertainty information caused by misclassification     

Nonlinear integrals with polynomial kernel and its applications

Nonlinear integrals (NIs) are useful integration tools. It can get a set of virtual values by projecting original data onto a virtual space for classification purpose using NIs. The classical NIs implement projection along a line with respect to the features. But, in many cases, the linear projection cannot achieve good performance for classification or regression due to the limitation of the integrand. The linear function used for the integrand is just a special type of function with respect to the features. In this paper, we propose a nonlinear integrals with polynomial kernel (NIPK). A polynomial function with respect to the features is used as the integrand of NIs. It enables the projection to be along different types of curves to the virtual space so that the virtual values gotten by NIs can be better regularized and have higher separation power for classification. We use genetic algorithm to learn the fuzzy measures so that a larger solution space can be searched. To test the capability of the NIPK, we apply it to classification on several benchmark datasets and a bioinformatics project. Experiments show that there is evident improvement on performance for the NIPK compared to classical NIs. © 2011 Wiley Periodicals, Inc.     

Exploring the boundary region of tolerance rough sets for feature selection

Of all of the challenges which face the effective application of computational intelligence technologies for pattern recognition, dataset dimensionality is undoubtedly one of the primary impediments. In order for pattern classifiers to be efficient, a dimensionality reduction stage is usually performed prior to classification. Much use has been made of rough set theory for this purpose as it is completely data-driven and no other information is required; most other methods require some additional knowledge. However, traditional rough set-based methods in the literature are restricted to the requirement that all data must be discrete. It is therefore not possible to consider real-valued or noisy data. This is usually addressed by employing a discretisation method, which can result in information loss. This paper proposes a new approach based on the tolerance rough set model, which has the ability to deal with real-valued data whilst simultaneously retaining dataset semantics. More significantly, this paper describes the underlying mechanism for this new approach to utilise the information contained within the boundary region or region of uncertainty. The use of this information can result in the discovery of more compact feature subsets and improved classification accuracy. These results are supported by an experimental evaluation which compares the proposed approach with a number of existing feature selection techniques.     

PRISM – A novel framework for pattern recognition

In this paper, we introduce a new model of solving pattern recognition tasks called PRISM (Pattern Recognition using Information Slicing Method). The main concept behind PRISM is the slicing of information through multiple planes across different feature axes to generate a number of cells. The number of cells created and their volume depends upon the number partitions per axes. In this context we define resolution as the number of partitions per axes. In this paper, we make the following contributions. First, we provide a brief survey of the class separability measures and feature partitioning schemes used for pattern recognition. Secondly, we define the PRISM framework and the algorithm for data assignment to cells. Thirdly, we detail four important concepts in PRISM: purity, neighbourhood separability, collective entropy, and data compactness. The first two measures define the data complexity, the next measure relates to uncertainty, and the last measure defines the alternative to statistical data variance in the PRISM framework. Fourthly, we investigate the variability in the estimates of these measures depending on the placement of partitions on each feature axis. Finally, we give an overview of experimental successes achieved with PRISM in the areas of classification complexity estimation and feature selection.     

Texture classification using fuzzy uncertainty texture spectrum

A new method using fuzzy uncertainty, which measures the uncertainty of the uniform surface in an image, is proposed for texture analysis. A grey-scale image can be transformed into a fuzzy image by the uncertainty definition. The distribution of the membership in a measured fuzzy image, denoted by the fuzzy uncertainty texture spectrum (FUTS), is used as the texture feature for texture analysis. To evaluate the performance of the proposed method. supervised texture classification and rotated texture classification are applied. Experimental results reveal high-accuracy classification rates and show that the proposed method is a good tool for texture analysis.     

Managing uncertainty when aggregating from pixels to objects: habitats,context-sensitive mapping and possibility theory

Object-oriented remote sensing software provides the user with flexibility in the way that remotely sensed data are classified through segmentation routines and user-specified fuzzy rules. This paper explores the classification and uncertainty issues associated with aggregating detailed ‘sub-objects’ to spatially coarser ‘super-objects’ in object-oriented classifications. We show possibility theory to be an appropriate formalism for managing the uncertainty commonly associated with moving from ‘pixels to parcels’ in remote sensing. A worked example with habitats demonstrates how possibility theory and its associated necessity function provide measures of certainty and uncertainty and support alternative realizations of the same remotely sensed data that are increasingly required to support different applications.     

多标记数据特征提取方法的核改进

针对多标记数据特征提取方法中输出核函数没有准确刻画标记间的相关性的问题,在充分度量标记间相关性的基础上,提出了两种新的输出核函数构造方法。第一种方法首先将多标记数据转化为单标记数据,并使用标记集合来刻画标记间的相关性;然后从损失函数的角度出发定义新的输出核函数。第二种方法是利用互信息来度量标记间的两两相关性,在此基础上进一步构造新的输出核函数。3个多标记数据集上2种分类器的实验结果表明,与原有核函数对应的多标记特征提取方法相比,基于损失函数的输出核函数对应的特征提取方法性能最好,5个评价指标的性能平均提高了10%左右, 尤其在Yeast数据集上,Coverage指标下降幅度达到了30%左右;基于互信息的输出核函数次之,性能平均提高了5%左右。实验结果表明,基于新的输出核函数的特征提取方法能够更加有效地提取特征,并进一步简化分类器的学习过程,提高分类器的泛化性能。     

基于类决策树分类的特征层融合识别算法

针对雷达组网量测数据不确定性大、信息不完备等特点, 基于决策树分类算法的思想, 创建类决策树的概念, 提出一种基于类决策树分类的特征层融合识别算法. 所给出的算法无需训练样本, 采用边构造边分类的方式, 选取信 息增益最大的属性作为分类属性对量测数据进行分类, 实现了对目标的识别. 该算法能够处理含有空缺值的量测数据, 充分利用量测数据的特征信息. 仿真实验结果表明, 类决策树分类算法是一种简单有效的特征层融合识别算法.

     

Uncertainty measures for fuzzy relations and their applications

Relations and relation matrices are important concepts in set theory and intelligent computation. Some general uncertainty measures for fuzzy relations are proposed by generalizing Shannon's information entropy. Then, the proposed measures are used to calculate the diversity quantity of multiple classifier systems and the granularity of granulated problem spaces, respectively. As a diversity measure, it is shown that the fusion system whose classifiers are of little similarity produces a great uncertainty quantity, which means that much complementary information is achieved with a diverse multiple classifier system. In granular computing, a “coarse–fine” order is introduced for a family of problem spaces with the proposed granularity measures. The problem space that is finely granulated will get a great uncertainty quantity compared with the coarse problem space. Based on the observation, we employ the proposed measure to evaluate the significance of numerical attributes for classification. Each numerical attribute generates a fuzzy similarity relation over the sample space. We compute the condition entropy of a numerical attribute or a set of numerical attribute relative to the decision, where the greater the condition entropy is, the less important the attribute subset is. A forward greedy search algorithm for numerical feature selection is constructed with the proposed measure. Experimental results show that the proposed method presents an efficient and effective solution for numerical feature analysis.     

脑机接口中脑电信号的特征提取和模式分类

从智能处理与不确定性的角度, 探讨了脑机接口中的核心问题-EEG模式特征的识别和分类. 针对EEG模式分类中所存在的不确定性问题, 从EEG的特征提取和分类模型构建两个方面进行了分析, 并提出了解决问题的方法和对策. 以P300成分为例, 从导联选择、滤波处理和时间窗处理三方面进行特征提取, 采用贝叶斯线性判别分析的方法进行模式分类. 最后以第三届脑机接口竞赛P300字符输入的数据为实验, 分别采用3种不同的方法进行数据分析, 通过分类准确率和不同重复次数下性能的比较, 实验结果表明了本文特征提取和模式分类方法的有效性.     

MEASUREMENT OF POSSIBILITY DISTRIBUTIONS

The problem of assessing numerical values of possibility distributions is considered in the paper. Particularly, we are interested in estimating the possibility values from a data set. The proposed estimation methods are based on the idea of transforming a probability distribution (obtained from the data set) into a possibility one. They also take into account that smaller data base size involve a greater uncertainty about the model and therefore, less precise assessments should be obtained in such cases. Moreover, in order to validate the estimated joint possibility distribution, a set of properties which guarantee that we obtain reasonable results will be studied. Finally, we are interested in analyzing the feasibility of the decisions or the conclusions that can be obtained by manipulating the estimated possibility distribution, so that some of the properties of this distribution, after applying to it the marginalization and conditioning operators, are also studied.     

基于结构上下文的模糊神经网络自动目标检测方法

提出了一种基于结构上下文的模糊神经网络(SCFNN)自动目标检测方法。模糊神经网络方法既具有神经网络的自适应性、并行性、鲁棒性、容错性、优化等优点，又集成了模糊集理论运用知识、规则描述解决系统不确定性的优点，因此成为图像处理和模式识别的一种强有力工具。使用模糊测度作为神经网络的目标函数可以有效地描述像素类别的不确定性，从而通过使其最小实现图像分类优化。对网络神经元加权过程进行结构上下文信息约束可以充分减小图像信息尤其是目标边缘等特性包含丰富信息的损失，有效地保持目标的轮廓和形状等属性，改善目标检测的误检率。针对目标遥感图像的实验，验证了SCFNN方法具有很好的自动目标检测能力，而相对于传统神经网络方法，具有有效的不确定性解决能力和更好的目标形状保持能力。