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De-combination of belief function based on optimization

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Chinese Journal of Aeronautics 2022年第5期35卷 179-193页

作者： Xiaojing FAN Deqiang HAN Yi YANG jean dezert School of Automation Science and Engineering Xi’an Jiaotong UniversityXi’an 710049China SKLSVMS School of AerospaceXi’an Jiaotong UniversityXi’an 710049China ONERA The French Aerospace LabPalaiseau 91761France

In the theory of belief functions,the evidence combination is a kind of decision-level information *** two or more Basic Belief Assignments(BBAs)originated from different information sources,the combination rule is used to combine them to expect a better decision *** only a combined BBA is given and original BBAs are discarded,if one wants to analyze the difference between the information sources,evidence de-combination is needed to determine the original *** de-combination can be considered as the inverse process of the information *** paper focuses on such a defusion of information in the theory of belief *** is an under-determined problem if only the combined BBA is *** this paper,two optimization-based approaches are proposed to de-combine a given BBA according to the criteria of divergence maximization and information maximization,*** new proposed approaches can be used for two or more information *** numerical examples and an example of application are provided to illustrate and validate our approaches.

关键词： Belief functions De-combination Divergence maximization Information fusion Information maximization

Novel moderate transformation of fuzzy membership function into basic belief assignment

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Chinese Journal of Aeronautics 2023年第1期36卷 369-385页

作者： Xiaojing FAN Deqiang HAN jean dezert Yi YANG School of Automation Science and Engineering Xi’an Jiaotong UniversityXi’an 710049China ONERA The French Aerospace LabPalaiseau 91761France SKLSVMS School of AerospaceXi’an Jiaotong UniversityXi’an 710049China

In information fusion,the uncertain information from different sources might be modeled with different theoretical *** one needs to fuse the uncertain information represented by different uncertainty theories,constructing the transformation between different frameworks is *** transformations of a Fuzzy Membership Function(FMF)into a Basic Belief Assignment(BBA)have been proposed,where the transformations based on uncertainty maximization and minimization can determine the BBA without preselecting the focal ***,these two transformations that based on uncertainty optimization emphasize the extreme cases of *** avoid extreme attitudinal bias,a trade-off or moderate BBA with the uncertainty degree between the minimal and maximal ones is more *** this paper,two moderate transformations of an FMF into a trade-off BBA are *** is the weighted average based transformation and the other is the optimization-based transformation with weighting mechanism,where the weighting factor can be user-specified or determined with some prior *** rationality and effectiveness of our transformations are verified through numerical examples and classification examples.

关键词： Basic belief assignment Belief functions Fuzzy membership function Information fusion Moderate transformation

Combination of classifiers with incomplete frames of discernment

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Chinese Journal of Aeronautics 2022年第5期35卷 145-157页

作者： Zhunga LIU Jingfei DUAN Linqing HUANG jean dezert Yongqiang ZHAO School of Automation Northwestern Polytechnical UniversityXi’an 710072China ONERA–The French Aerospace Lab Palaiseau 91761France

The methods for combining multiple classifiers based on belief functions require to work with a common and complete(closed)Frame of Discernment(Fo D)on which the belief functions are defined before making their *** theoretical requirement is however difficult to satisfy in practice because some abnormal(or unknown)objects that do not belong to any predefined class of the Fo D can appear in real classification *** classifiers learnt using different attributes information can provide complementary knowledge which is very useful for making the classification but they are usually based on different Fo *** order to clearly identify the specific class of the abnormal objects,we propose a new method for combination of classifiers working with incomplete frames of discernment,named CCIF for *** is a progressive detection method that select and add the detected abnormal objects to the training data *** one pattern can be considered as an abnormal object by one classifier and be committed to a specific class by another one,a weighted evidence combination method is proposed to fuse the classification results of multiple *** new method offers the advantage to make a refined classification of abnormal objects,and to improve the classification accuracy thanks to the complementarity of the *** experimental results are given to validate the effectiveness of the proposed method using real data sets.

关键词： Abnormal object Belief functions Classifier fusion Evidence theory Detection

Basic belief assignment approximations using degree of non-redundancy for focal element

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Chinese Journal of Aeronautics 2019年第11期32卷 2503-2515页

作者： Yi YANG Deqiang HAN jean dezert SKLSVMS School of AerospaceXi'an Jiaotong UniversityXi'an 710049China Center for Information Engineering Science Research XVan Jiaotong UniversityXi'an 710049China ONERA The French Aerospace LabChemin de la HunierePalaiseau F-91761France

Dempster-Shafer evidence theory, also called the theory of belief function, is widely used for uncertainty modeling and reasoning. However, when the size and number of focal elements are large, the evidence combination will bring a high computational complexity. To address this issue,various methods have been proposed including the implementation of more efficient combination rules and the simplifications or approximations of Basic Belief Assignments(BBAs). In this paper,a novel principle for approximating a BBA into a simpler one is proposed, which is based on the degree of non-redundancy for focal elements. More non-redundant focal elements are kept in the approximation while more redundant focal elements in the original BBA are removed first. Three types of degree of non-redundancy are defined based on three different definitions of focal element distance, respectively. Two different implementations of this principle for BBA approximations are proposed including a batch and an iterative type. Examples, experiments, comparisons and related analyses are provided to validate proposed approximation approaches.

关键词： BBA approximation Belief functions Evidence theory Focal element Non-redundancy

Evidential combination of augmented multi-source of information based on domain adaptation

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Science China(Information Sciences) 2020年第11期63卷 38-55页

作者： Linqing HUANG Zhunga LIU Quan PAN jean dezert School of Automation Northwestern Polytechnical University ONERA-The French Aerospace Lab

In the applications of domain adaptation(DA), there may exist multiple source domains, and each source domain usually provides some auxiliary information for object classification. The combination of such complementary knowledge from different source domains is helpful for improving the accuracy. We propose an evidential combination of augmented multi-source of information(ECAMI) method. The information sources are augmented at first by merging several randomly selected source domains to generate extra auxiliary information. We can obtain one piece of classification result with the assistance of each information source based on DA. Then these multiple classification results are combined by belief functions theory, which is expert at dealing with the uncertain information. Nevertheless, the classification results derived from different information sources may have different weights. The optimal weights are calculated by minimizing an given error criteria defined by the distance between the combination result and the ground truth using some training data. For each object, the augmented information sources will produce multiple classification results that will be discounted by the learnt weights under the belief functions framework. Then the combination of these discounted results is employed to make the final class decision. The effectiveness of ECAMI is evaluated with respect to some related methods based on several real data sets, and the experimental results show that ECAMI can significantly improve the classification accuracy.

关键词： information fusion domain adaptation evidence theory belief functions pattern classification

A new non-specificity measure in evidence theory based on belief intervals

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Chinese Journal of Aeronautics 2016年第3期29卷 704-713页

作者： Yang Yi Han Deqian jean dezert SKLSVMS School of AerospaceXi'an Jiaotong UniversityXi'an 710049China Center for Information Engineering Science Research Xi'an Jiaotong UniversityXi'an 710049China ONERA The Freneh Aerospace LabChemin de la HunireF-91761 PalaiseauFrance

In the theory of belief functions, the measure of uncertainty is an important concept, which is used for representing some types of uncertainty incorporated in bodies of evidence such as the discord and the non-specificity. For the non-specificity part, some traditional measures use for reference the Hartley measure in classical set theory; other traditional measures use the simple and heuristic function for joint use of mass assignments and the cardinality of focal elements. In this paper, a new non-specificity measure is proposed using lengths of belief intervals, which represent the degree of imprecision. Therefore, it has more intuitive physical meaning. It can be proved that our new measure can be rewritten in a general form for the non-specificity. Our new measure is also proved to be a strict non-specificity measure with some desired properties. Numerical examples, simulations, the related analyses and proofs are provided to show the characteristics and good properties of the new non-specificity definition. An example of an application of the new non- specificity measure is also presented.

关键词： Belief interval Evidence theoryImprecision Non-specificity Uncertainty

Combination of Qualitative Information with 2-Tuple Linguistic Representation in DSmT

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Journal of Computer Science & Technology 2009年第4期24卷 786-797页

作者：李新德 Florentin Smarandache jean dezert 戴先中 IEEE MOE Key Laboratory of Measurement and Control of CSE School of AutomationSoutheast University Mathematics and Sciences Department University of New Mexico200 College RoadGallupNM 87301 U.S.A. French Aerospace Research Lab. 29 Avenue de la Division Leclerc 92320 ChtillonFrance

Modern systems for information retrieval, fusion and management need to deal more and more with information coming from human experts usually expressed qualitatively in natural language with linguistic labels. In this paper, we propose and use two new 2-Tuple linguistic representation models （i.e., a distribution function model （DFM） and an improved Herrera-Martinez＇s model） jointly with the fusion rules developed in dezert-Smarandache Theory （DSmT）, in order to combine efficiently qualitative information expressed in term of qualitative belief functions. The two models both preserve the precision and improve the efficiency of the fusion of linguistic information expressing the global expert＇s opinion. However, DFM is more general and efficient than the latter, especially for unbalanced linguistic labels. Some simple examples are also provided to show how the 2-Tuple qualitative fusion rules are performed and their advantages.

关键词： dezert-Smarandache Theory (DSmT) information fusion qualitative reasoning linguistic labels

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一种飞机图像目标多特征信息融合识别方法

自动化学报 2012年第8期38卷 1298-1307页

作者：李新德杨伟东 dezert jean 东南大学自动化学院复杂工程测量与控制教育部重点实验室法国国家航天航空研究中心

提出了一种基于概率神经网络(Probabilistic neural networks,PNN)和DSmT推理(dezert-Smarandache theory)的飞机图像目标多特征融合识别算法.针对提取的多个图像特征量,利用数据融合的思想对来自图像目标各个特征量提供的信息进行融合... 详细信息

提出了一种基于概率神经网络(Probabilistic neural networks,PNN)和DSmT推理(dezert-Smarandache theory)的飞机图像目标多特征融合识别算法.针对提取的多个图像特征量,利用数据融合的思想对来自图像目标各个特征量提供的信息进行融合处理.首先,对图像进行二值化预处理,并提取Hu矩、归一化转动惯量、仿射不变矩、轮廓离散化参数和奇异值特征5个特征量;其次,针对DSmT理论中信度赋值构造困难的问题,利用PNN网络,构造目标识别率矩阵,通过目标识别率矩阵对证据源进行信度赋值;然后,用DSmT组合规则在决策级层进行融合,从而完成对飞机目标的识别;最后,在目标图像小畸变情形下,将本文提出的图像多特征信息融合方法和单一特征方法进行了对比测试实验,结果表明本文方法在同等条件下正确识别率得到了很大提高,同时达到实时性要求,而且具有有效拒判能力和目标图像尺寸不敏感性.即使在大畸变情况下,识别率也能达到89.3%.

关键词：信息融合目标识别 dezert-Smarandache推理飞机图像概率神经网络

一种快速分层递阶DSmT近似推理融合方法(C)

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华中科技大学学报（自然科学版） 2011年第S2期39卷 150-152,156页

作者：李新德杨伟东 jean dezert 东南大学复杂工程系统测量与控制教育部重点实验室江苏南京210096 法国航空实验室帕莱索赛代克斯f91761

针对超幂集空间中部分不确定焦元或者混合焦元具有信度赋值的情形,将混合焦元转化为统一形式;根据纯不确定焦元平分原则进行平分信度赋值,并将新的或固有的冲突焦元的信度赋值分配到相应的单子焦元上;利用二叉树分组技术对单子焦元进行... 详细信息

针对超幂集空间中部分不确定焦元或者混合焦元具有信度赋值的情形,将混合焦元转化为统一形式;根据纯不确定焦元平分原则进行平分信度赋值,并将新的或固有的冲突焦元的信度赋值分配到相应的单子焦元上;利用二叉树分组技术对单子焦元进行刚性分组,实现细粒度超向粗粒度超幂集空间的映射;运用DSmT组合规则和比例冲突分配规则对粗化超幂集空间的多个信息源进行融合,保存该融合结果作为父子之间节点连接权值;对每个分组焦元信度赋值归一化处理,通过设定树的深度,来确定分层递阶的次数;最后从计算效率、信息损失和相似度的角度分别就新、老方法进行比较,结果验证了新方法的优越性.

关键词：近似推理信息融合分层递阶 dezert-Smarandache理论不确定焦元