一种度量广义基本概率赋值冲突的方法

Dempster-Shafer(D-S)证据理论在组合冲突信息时,会得出与直觉相反的结论,为此研究人员提出很多改进方法,但是如何度量证据之间的冲突程度却常常被人们忽视.在分析现有冲突系数的基础上,在推广幂集空间框架下提出了一个冲突距离系数,用来刻画证据之间的冲突程度.进一步提出了合理的冲突度量参数应满足的判定准则,通过两种典型的悖论情况,分析了经典冲突系数和二元组冲突表示方法的不足,说明所提出的冲突系数不但满足判定准则,而且在判断冲突使用Dempster组合规则方面可以达到二元组表示方法的同等效果,甚至在判断冲突使用Dezert-Smarandache theory(DSmT)方面可以超过二元组表示方法的效果.     

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。     

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.     

A flexible rule for evidential combination in Dempster–Shafer theory of evidence

Dempster’s combination rule in Dempster–Shafer theory of evidence is widely used to combine multiple pieces of evidence. However, when the evidence is severely conflicting, the result could be counter-intuitive. Thus, many alternative combination rules have been proposed to address this issue. Nevertheless, the existing ones sometimes behave not very well. This may be because they do not hold some essential properties. To this end, this paper firstly identifies some of the important properties. Then, following the cues from these properties, we propose a novel evidential combination rule as a remediation of Dempster’s combination rule in Dempster–Shafertheory. Our new rule is based on the concept of complete conflict (we introduced in this paper), Dempster’s combination rule, and the concept of evidence weight. Moreover, we illustrate the effectiveness of our new rule by using it to successfully resolve well-known Zadeh’s counter-example, which is against Dempster’s combination rule. Finally, we confirm the advantages of our method over the existing methods through some examples.     

基于冲突强度和非正则化的证据合成方法研究

证据推理广泛应用于不确定推理和数据融合等许多方面,但D-S合成规则对于高冲突证据的处理不是十分合理的。论文在分析D-S合成规则以及一些改进方法的基础上,提出了一种基于冲突强度和非正则化的冲突证据合成规则,并引入确定度的概念来衡量合成的效果。仿真实验结果表明,该规则比D-S合成规则有了明显的改进。     

Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy

Multi-sensor data fusion technology plays an important role in real applications. Because of the flexibility and effectiveness in modeling and processing the uncertain information regardless of prior probabilities, Dempster–Shafer evidence theory is widely applied in a variety of fields of information fusion. However, counter-intuitive results may come out when fusing the highly conflicting evidences. In order to deal with this problem, a novel method for multi-sensor data fusion based on a new belief divergence measure of evidences and the belief entropy was proposed. First, a new Belief Jensen–Shannon divergence is devised to measure the discrepancy and conflict degree between the evidences; then, the credibility degree can be obtained to represent the reliability of the evidences. Next, considering the uncertainties of the evidences, the information volume of the evidences are measured by making use of the belief entropy to indicate the relative importance of the evidences. Afterwards, the credibility degree of each evidence is modified by taking advantage of the quantitative information volume which will be utilized to obtain an appropriate weight in terms of each evidence. Ultimately, the final weights of the evidences are applied to adjust the bodies of the evidences before using the Dempster’s combination rule. A numerical example is illustrated that the proposed method is feasible and effective in handling the conflicting evidences, where the belief value of target increases to 99.05%. Furthermore, an application in fault diagnosis is given to demonstrate the validity of the proposed method. The results show that the proposed method outperforms other related methods where the basic belief assignment (BBA) of the true target is 89.73%.     

决策距离修正下的弱决策证据合成方法

针对含弱决策的证据融合在低冲突情况下仍出现反直观结果的问题,提出一种决策距离修正下的证据合成方法.首先,给出弱决策证据定义,提出一种名为决策距离的新度量方法,可表述单证据的决策,通过融合Jousselme距离可更有效地描述弱决策证据与其他证据间的差异;然后,根据检测弱决策证据和一票否决证据是否同时存在,提供两种不同的修正系数,可有效扩大多数证据与其他证据修正系数的差距,削弱一票否决证据的影响;最后,对证据源修正并合成.实验结果表明,该合成方法能较好地解决弱决策证据融合问题,融合结果收敛快,决策更可靠,不确定性小,是对现有研究的良好补充.     

基于选择判据和贴近度的D-S证据融合方法

针对传统D-S证据理论难以融合高度冲突证据的问题,并考虑到证据正常时Dempster规则具有优越的聚焦性能,提出了一种基于选择判据和贴近度的证据融合方法。把贴近度概念引入到D-S证据合成中,通过证据的一致性度量来计算证据的权重,从而实现了冲突证据的加权融合。同时提出了证据修正的选择判据,将证据分成冲突与非冲突两类,对冲突的证据进行修正后再进行合成,而非冲突证据可直接进行合成。通过实例验证表明,所提出的方法不但保持了Dempster规则优越的信息聚焦性能,而且较好的解决了冲突证据的合成问题。     

基于局部冲突分配策略的证据合成法则的改进

针对证据合成法则在证据高度冲突情况下常得出有悖常理的结论,通过理论分析、对比多种改进的合成方法,提出一种基于局部冲突分配策略的组合规则,采用以冲突焦元在局部冲突组合证据中所占的实际比值为权重的方法,将冲突在产生冲突焦元中分解。实验结果证明,即使在证据高度冲突的情况下,改进后的合成法则依然能够取得理想的合成结果。     

基于证据可信度的D-S证据理论合成规则

Dempster合成规则是一种经典D-S理论的合成规则,但在参与合成的证据间具有较大的不一致性或冲突时,则不能使用或得出明显不合理的结果,引起错误决策。为了解决冲突证据的合成问题,提出了一种基于证据可信度的合成规则。通过算例仿真,该规则可以有效解决两个或两个以上的证据冲突问题,而且计算简单,计算量小。     

一种基于ISODATA聚类和改进相似度的证据推理方法

针对智能信息处理中Dempster组合规则不能处理高度冲突的问题, 从内、外证据不确定性分析的角度深入揭示了证据冲突产生的原因, 即证据的冲突性不仅仅根源于证据间的矛盾, 也与证据自身的不确定性密切相关, 提出了一种同时考虑证据自冲突和外部冲突的相似性测度, 然后利用新测度计算证据的众信度, 对证据源进行修正;与此同时, 根据原始证据间的聚类特性, 利用迭代自组织数据分析技术(Iterative selforganizing data analysis techniques algorithm, ISODATA)聚类方法进行聚类, 然后利用Dempster组合规则合成每一聚类中所有证据为证据代表, 并综合众信度和证据在该聚类的频度计算可靠度, 最后, 利用统一组合规则合成证据代表.并通过大量的算例, 同其他方法和自身改进前后进行深入比较, 优势比较明显, 有效地解决了冲突证据合成出现的问题.     

一种新的证据冲突分析方法

当证据高度冲突时,使用DS组合规则经常会得到错误的结果,因此对DS证据理论的合成方法进行改进成为人们研究的重点.但是如何去度量或确定证据之间冲突的程度却常常被人忽视.在以往的研究中均使用冲突系数k作为表征证据之间冲突的量,但是研究结果表明,k不能很好的描述证据之间的冲突.对表征证据冲突的变量进行了研究,提出了一种新的表征证据之间冲突的变量-关联系数,基于偏熵和混合熵,定义了关联系数,该系数可以定量的表示证据之间的冲突.当关联系数接近1时证据之间冲突很小,当关联系数接近0时证据之间高度冲突.算例验证了所提出的基于关联系数的冲突表示方法的有效性.     

基于分类修正的多证据合成方法

鉴于传统冲突量参数无法有效地衡量证据间的相似程度, 提出一种基于分类修正的多证据合成方法, 以解决证据合成中的高冲突悖论和“0”悖论. 首先, 利用证据距离参数、冲突量参数和方向角度参数共同衡量各证据间的相似程度, 将证据分为一致证据、不冲突证据、低冲突证据以及高冲突证据4 类; 然后, 利用3 个参数赋予各类证据不同的修正系数; 最后, 利用Dempster 规则对修正后的证据进行合成. 算例分析表明, 所提出的方法能够较好地解决高冲突悖论和“0”悖论, 而且保留了证据理论优良的数学性质.     

An integrated information fusion approach based on the theory of evidence and group decision-making

Dempster–Shafer theory of evidence has been employed as a major method for reasoning with multiple evidence. The Dempster’s rule of combination is however incapable of managing highly conflicting evidence coming from different information sources at the normalization step. Extending current rules, we incorporate the ideas of group decision-making into the theory of evidence and propose an integrated approach to automatically identify and discount unreliable evidence. An adaptive robust combination rule that incorporates the information contained in the consistent focal elements is then constructed to combine such evidence. This rule adjusts the weights of the conjunctive and disjunctive rules according to a function of the consistency of focal elements. The theoretical arguments are supported by numerical experiments. Compared to existing combination rules, the proposed approach can obtain a reasonable and reliable decision, as well as the level of uncertainty about it.     

基于加权证据距离的高度冲突证据组合方法

为了有效融合高度冲突的证据,以Murphy方法和邓勇加权平均法为基础,提出了一种新的基于加权证据距离的证据组合方法。用Murphy方法确定各证据体的权重,采用修正的City Block距离加权平均求证据间的两两距离,进而获取各证据被其他所有证据支持的程度,归一化各证据的总支持度作为该证据的权重,对多源证据加权平均后再利用Dempster组合规则实现信息融合。实验结果表明,该方法能够更加有效快速地识别出目标,拥有更快的收敛速度。     

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。     

基于新的证据冲突衡量的加权证据融合方法

对冲突证据使用Dempster-Shafer 证据理论进行融合的前提是对冲突证据作出正确衡量, 确定证据之间冲突的程度. 在分析现有的冲突衡量方法基础上, 提出一种基于新的证据冲突衡量的加权证据融合方法. 该方法通过相似性测度来衡量证据间的冲突程度; 然后确定各证据的可信度, 再加权修正证据; 最后用Dempster 组合规则进行融合. 算例表明, 该方法能正确衡量证据冲突程度, 有效地解决冲突证据的融合问题, 提高收敛速度和精度.

     

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。     

解决冲突证据的两级组合方法

针对DS理论(DST)中Dempster组合规则在处理高冲突证据时的不足,提出一种解决冲突证据的两级组合方法。该方法将高冲突和低冲突区别对待,在第一级组合中采用基于DSm理论(DSmT)的PCR6规则,化解可能的高冲突证据;在第二级组合中采用Dempster规则,保证良好的收敛速度和计算性能,从而合理、有效地处理各种程度的冲突证据。通过算例分析验证了该方法的有效性。     

Context-dependent combination of sensor information in Dempster–Shafer theory for BDI

There has been much interest in the belief–desire–intention (BDI) agent-based model for developing scalable intelligent systems, e.g. using the AgentSpeak framework. However, reasoning from sensor information in these large-scale systems remains a significant challenge. For example, agents may be faced with information from heterogeneous sources which is uncertain and incomplete, while the sources themselves may be unreliable or conflicting. In order to derive meaningful conclusions, it is important that such information be correctly modelled and combined. In this paper, we choose to model uncertain sensor information in Dempster–Shafer (DS) theory. Unfortunately, as in other uncertainty theories, simple combination strategies in DS theory are often too restrictive (losing valuable information) or too permissive (resulting in ignorance). For this reason, we investigate how a context-dependent strategy originally defined for possibility theory can be adapted to DS theory. In particular, we use the notion of largely partially maximal consistent subsets (LPMCSes) to characterise the context for when to use Dempster’s original rule of combination and for when to resort to an alternative. To guide this process, we identify existing measures of similarity and conflict for finding LPMCSes along with quality of information heuristics to ensure that LPMCSes are formed around high-quality information. We then propose an intelligent sensor model for integrating this information into the AgentSpeak framework which is responsible for applying evidence propagation to construct compatible information, for performing context-dependent combination and for deriving beliefs for revising an agent’s belief base. Finally, we present a power grid scenario inspired by a real-world case study to demonstrate our work.