基于信任函数理论的修正融合目标识别算法

针对信任函数理论中经典Dempster组合规则难以有效融合高冲突证据并存在焦元基模糊问题,提出了一种基于信任函数理论的修正融合目标识别算法.修正融合算法在对相容命题进行组合时,考虑了焦元基的影响,使基本信任质量合理地向基数较小的焦元命题聚焦,以避免焦元基模糊问题;在对冲突命题进行组合时,对命题进行倾向性分析并对局部冲突采用局部分配的策略,以有效融合高冲突证据.算例与仿真比较分析验证了此修正融合目标识别算法的合理有效性和优越性.     

一种基于修改模型的冲突证据组合方法

为解决Dempster-Shafer证据理论在对高度冲突的证据进行融合时可能导致与直观结果相悖的问题,本文提出一种有效处理冲突证据的融合方法。通过引入距离函数,确定证据之间的相互支持度,进而确定证据的权值。采用平均证据代替冲突证据,通过证据的权值修改证据源模型,然后基于Dempster组合规则进行证据组合,以减少冲突证据在组合规则中的作用能力,有效降低干扰对最终融合结果的影响,充分利用了原始证据信息,使得组合结果收敛到正确的目标的效率比较高。     

一种有效折扣证据源的冲突证据合成方法

为解决证据组合规则中一票否决和弱决策证据在低冲突情况下出现的反直观推理的现象，提出一种有效折扣证据源的冲突证据合成方法。首先根据证据的信任函数和似然函数求得证据间的相似度，然后求出证据之间的支持程度，并确定折扣因子，最后采用Dempster组合规则合成利用折扣因子修正后的证据源。数值算例分析结果表明，改进后的证据组合方法可以有效地处理证据冲突。     

基于向量冲突表示方法的证据组合规则

针对Dempster组合规则在高冲突证据融合的情况下常常会得到违背直觉的结果,提出了一种基于向量冲突表示方法的Dempster(VCRD)组合规则。首先,通过实例分析了冲突因子和Jousselme距离存在的不足;然后,利用证据向量的相似性和差异性共同衡量证据之间的冲突程度,通过证据之间的冲突程度确定修正证据的权重因子,对融合证据进行预处理;最后,利用Dempster组合规则进行融合。理论分析和仿真实验结果表明:与Dempster组合规则及其它改进算法相比,VCRD组合规则能够合理地处理高冲突证据情况下的融合问题,降低了决策风险。     

基于多准则排序融合的证据组合方法

Dempster-Shafer证据理论在信息融合领域有着广泛而重要的应用, 但传统Dempster证据组合规则往往会引发一系列反直观结果问题, 如冲突悖论、信任偏移悖论以及证据吸收悖论等. 针对这一问题, 提出了一种基于多准则排序融合的证据组合新方法. 该方法综合利用了证据精度、证据可信度以及证据自冲突程度等指标评价待组合证据体,并以选择性融合的方式获取最终的组合结果. 仿真结果和相关分析表明,所提方法是合理有效的.     

一种基于优化权重证据组合的目标综合识别方法

针对高度冲突识别信息 Dempster 规则融合失效问题,分析了有关改进方法及其存在的不足,提出了一种新的证据组合方法。新方法首先根据证据之间 pignistic 概率距离和基于信息熵的证据清晰度综合确定各证据权重系数,然后使用该权重系数对证据源进行修正,最后将修正后的加权平均证据进行 Dempster 规则组合。仿真实验结果表明新方法在目标综合识别中合成结果更好,收敛速度更快。     

基于预处理模式的D-S证据理论改进方法

D-S证据理论是决策融合的主要方法之一,但典型的D-S理论不大适应高冲突证据组合.本文提出一种基于预处理模式的方法,在利用Dempster组合规则进行证据组合之前,将冲突焦元的基本概率赋值部分转移到焦元并集,采用证据之间的冲突额度来确定证据组合顺序.由于该方法将冲突化解为不确定的知识表示,可以处理冲突证据的组合问题.     

一种改进的D-S证据组合规则

根据D-S证据组合规则失效问题和现有的处理方法的不足,提出一种新的证据组合规则.在证据冲突较小时采用Dempster组合规则;证据冲突较大时,按新证据在全部证据中所占的比例来分配冲突,避免了因冲突较大而产生的失效问题.实验表明,新规则与现有的冲算处理方法相比,算法更简单,融合结果更有效.     

基于证据冲突度的多传感器冲突信息组合方法*

针对Dempster组合规则在多传感器冲突信息融合方面的不足,提出了改进的证据冲突的定义及基于冲突系数和Jousselme距离的证据冲突度的计算公式,给出了一种新的基于证据冲突度的证据加权融合方法。该方法首先利用证据冲突度构造证据相互支持度矩阵,进而计算证据的权重,最后利用Dempster规则对加权修正后的证据进行融合。数值实例表明：该方法可以有效融合高冲突信息,与Dempster组合规则和几种典型的加权证据融合方法相比,具有更快的收敛速度,而且收敛效果更好。     

一种新的证据融合方法及在目标跟踪中的应用

为了有效融合高度冲突的证据,本文在余弦相似度和K-L距离基础上提出一种证据自适应融合方法.首先联合余弦距离和经典冲突系数定义了一种新的证据冲突衡量标准;然后利用K-L距离获得待组合证据的权重,提出一种基于序贯式的证据组合方法.而后考虑到Dempster组合规则可以有效融合低冲突证据,为使新的组合方法和Dempster组合规则发挥各自的优势,提出了一种组合规则自适应切换的融合方法.最后基于AMI语料库对本文融合方法的有效性进行了验证.实验结果表明:相比传统的证据理论融合方法,本文方法具有较好的准确性和稳定性,可满足视频跟踪的应用需求.     

Belief function combination and conflict management

Within the framework of evidence theory, data fusion consists in obtaining a single belief function by the combination of several belief functions resulting from distinct information sources. The most popular rule of combination, called Dempster's rule of combination (or the orthogonal sum), has several interesting mathematical properties such as commutativity or associativity. However, combining belief functions with this operator implies normalizing the results by scaling them proportionally to the conflicting mass in order to keep some basic properties. Although this normalization seems logical, several authors have criticized it and some have proposed other solutions. In particular, Dempster's combination operator is a poor solution for the management of the conflict between the various information sources at the normalization step. Conflict management is a major problem especially during the fusion of many information sources. Indeed, the conflict increases with the number of information sources. That is why a strategy for re-assigning the conflicting mass is essential. In this paper, we define a formalism to describe a family of combination operators. So, we propose to develop a generic framework in order to unify several classical rules of combination. We also propose other combination rules allowing an arbitrary or adapted assignment of the conflicting mass to subsets.     

DEMPSTER’S RULE AS SEEN BY LITTLE COLORED BALLS

Dempster’s rule is traditionally interpreted as an operator for fusing belief functions. While there are different types of belief fusion, there has been considerable confusion regarding the exact type of operation that Dempster’s rule performs. Many alternative operators for belief fusion have been proposed, where some are based on the same fundamental principle as Dempster’s rule, and others have a totally different basis, such as the cumulative and averaging fusion operators. In this article, we analyze Dempster’s rule from a statistical and frequentist perspective and compare it with cumulative and averaging belief fusion. We prove, and illustrate by examples on colored balls, that Dempster’s rule in fact represents a method for serial combination of stochastic constraints. Consequently, Dempster’s rule is not a method for cumulative fusion of belief functions under the assumption that subjective beliefs are an extension of frequentist beliefs. Having identified the true nature of Dempster’s rule, appropriate applications of Dempster’s rule of combination are described such as the multiplication of orthogonal belief functions, and the combination of preferences dictated by different parties.     

一种基本概率指派的模糊生成及其在数据融合中的应用

DS证据组合规则可以在没有先验信息的情况下进行融合,这一优点使得DS证据理论在多传感器融合系统中应用非常广泛.但是各个证据的基本概率指派如何生成仍然是一个有待解决的问题.本文基于模糊匹配,提出了一种基本概率指派生成方法,并应用到多传感器目标识别中.用一个多传感器目标识别的实验表明:所提出的方法可以合理地生成基本概率指派,能够准确的识别目标.     

Dempster规则的有效性和限制

1 引言 Dempster-Shafer证据理论(以下简称证据理论)是在A.P.Dempster提出的“上、下概率”及其合成规则的基础上由G.Shafer在其1976年出版的专著《证据的数学理论》中建立起来的。80年代初,SRI的J.Lowrance等人将证据理论引入人工智能;J.Gordon和E.Shortliffe在专家系统的框架中研究了证据推理。此后,证据理论逐渐发展成为一类重要的不确定性推理方法。现在,基于证据理论的不确定性处理方法已是设计专家系统及其它智能系统的标准工具之一。     

On the Dempster-Shafer evidence theory and non-hierarchicalaggregation of belief structures

The Dempster's rule of combination is a widely used technique to integrate evidence collected from different sources. In this paper, it is shown that the values of certain functions defined on a family of belief structures decrease (by scale factors depending on the degree of conflict) when the belief structures are combined according to the Dempster's rule. Similar results also hold when an arbitrary belief structure is prioritized while computing the combination. Furthermore, the length of the belief-plausibility interval is decreased during a nonhierarchical aggregation of belief structures. Several types of inheritance networks are also proposed each of which allows considerable flexibility in the choice of prioritization     

Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence

Dempster's rule plays a central role in the theory of belief functions. However, it assumes the combined bodies of evidence to be distinct, an assumption which is not always verified in practice. In this paper, a new operator, the cautious rule of combination, is introduced. This operator is commutative, associative and idempotent. This latter property makes it suitable to combine belief functions induced by reliable, but possibly overlapping bodies of evidence. A dual operator, the bold disjunctive rule, is also introduced. This operator is also commutative, associative and idempotent, and can be used to combine belief functions issues from possibly overlapping and unreliable sources. Finally, the cautious and bold rules are shown to be particular members of infinite families of conjunctive and disjunctive combination rules based on triangular norms and conorms.     

Robust combination rules for evidence theory

Dempster’s rule of combination in evidence theory is a powerful tool for reasoning under uncertainty. Since Zadeh highlighted the counter-intuitive behaviour of Dempster’s rule, a plethora of alternative combination rules have been proposed. In this paper, we propose a general formulation for combination rules in evidence theory as a weighted sum of the conjunctive and disjunctive rules. Moreover, with the aim of automatically accounting for the reliability of sources of information, we propose a class of robust combination rules (RCR) in which the weights are a function of the conflict between two pieces of information. The interpretation given to the weight of conflict between two BPAs is an indicator of the relative reliability of the sources: if the conflict is low, then both sources are reliable, and if the conflict is high, then at least one source is unreliable. We show some interesting properties satisfied by the RCRs, such as positive belief reinforcement or the neutral impact of vacuous belief, and establish links with other classes of rules. The behaviour of the RCRs over non-exhaustive frames of discernment is also studied, as the RCRs implicitly perform a kind of automatic deconditioning through the simple use of the disjunctive operator. We focus our study on two special cases: (1) RCR-S, a rule with symmetric coefficients that is proved to be unique and (2) RCR-L, a rule with asymmetric coefficients based on a logarithmic function. Their behaviours are then compared to some classical combination rules proposed thus far in the literature, on a few examples, and on Monte Carlo simulations.     

On the fusion of imprecise uncertainty measures using belief structures

Our interest is in the fusion of information from multiple sources when the information provided by the individual sources is expressed in terms of an imprecise uncertainty measure. We observe that the Dempster-Shafer belief structure provides a framework for the representation of a wide class of imprecise uncertainty measures. We then discuss the fusion of multiple Dempster-Shafer belief structures using the Dempster rule and note the problems that can arise when using this fusion method because of the required normalization in the face of conflicting focal elements. We then suggest some alternative approaches fusing multiple belief structures that avoid the need for normalization.     

Idempotent conjunctive combination of belief functions: Extending the minimum rule of possibility theory

When conjunctively merging two belief functions concerning a single variable but coming from different sources, Dempster rule of combination is justified only when information sources can be considered as independent. When dependencies between sources are ill-known, it is usual to require the property of idempotence for the merging of belief functions, as this property captures the possible redundancy of dependent sources. To study idempotent merging, different strategies can be followed. One strategy is to rely on idempotent rules used in either more general or more specific frameworks and to study, respectively, their particularization or extension to belief functions. In this paper, we study the feasibility of extending the idempotent fusion rule of possibility theory (the minimum) to belief functions. We first investigate how comparisons of information content, in the form of inclusion and least-commitment, can be exploited to relate idempotent merging in possibility theory to evidence theory. We reach the conclusion that unless we accept the idea that the result of the fusion process can be a family of belief functions, such an extension is not always possible. As handling such families seems impractical, we then turn our attention to a more quantitative criterion and consider those combinations that maximize the expected cardinality of the joint belief functions, among the least committed ones, taking advantage of the fact that the expected cardinality of a belief function only depends on its contour function.