An improved evidence fusion algorithm in multi-sensor systems

Multi-sensor information fusion plays an important role in practical application. Although D-S evidence theory can handle this information fusion task regardless of prior knowledge, counter-intuitive conclusions may arise when dealing with highly conflicting evidence. To address this weakness, an improved algorithm of evidence theory is proposed. First, a new distribution distance measurement method is first proposed to measure the conflict between the evidences, and the credibility degree of the evidences can be obtained. Next, a modified information volume calculation method is also introduced to measure the effect of the evidence itself, and the information volume of the evidences can be generated. Afterwards, the credibility degree of each evidence can be modified based on the information volume to obtain the weight of each evidence. Ultimately, the weights of the evidences will be used to adjust the body of evidence before fusion. A numerical example for engine fault diagnosis exhibits the availability and effectiveness of the proposed method, where the BPA of the true fault is 89.680%. Furthermore, an application for target recognition is given to show the validity of the proposed algorithm, where the BPA of the true target is 98.948%. The experimental results show that the proposed algorithm has the best performance than other methods.

     

基于信息融合的罪案关联证据推理模型

针对传统犯罪案件中出现的冲突证据难以处理的情况,提出一种基于证据可信度和灰色关联的冲突证据融合处理方法;基于相似性视角的灰色关联度作为证据间的联系,采用改变证据源的证据组合规则来衡量证据源中各个证据之间的贴近度;考虑到证据的可信度,提出新的基于证据贴近度的权重确定方法,以证据的可信度作为权重,对参与融合的证据的基本概率分配函数进行加权平均,使证据融合收敛速度更快,并提升融合效果.最后以安徽省某市的入室盗窃犯罪案件为例,运用基于信息融合的关联证据推理方法处理案件中的冲突证据问题,验证了所提出方法的合理性和有效性.     

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.     

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.

     

A class of fuzzy measures generated from a Dempster–Shafer belief structure

Here the Dempster–Shafer belief structure is viewed as providing partial information about the underlying fuzzy measure associated with a uncertain variable. In this perspective there exists many possible fuzzy measures that can be associated with a Dempster–Shafer belief structure. Typically only two of these measures have been made explicit, those being the measure of belief and plausibility. Here we introduce a whole class of fuzzy measures that can be associated with a Dempster–Shafer belief structure. As an aid to choosing between these myriad of possibilities we discuss the entropy of a fuzzy measure. ©1999 John Wiley & Sons, Inc.     

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。     

考虑决策者时序偏好的时域证据融合方法

针对时域不确定信息的融合难题，为充分体现时域信息融合的动态性特点和时间因素对融合的影响，在证据理论的基础上，提出一种考虑决策者时序偏好的时域证据融合方法。首先将决策者对时序的偏好融入时域证据融合，通过分析时域证据序列的特点，在定义时序记忆因子的基础上，对决策者的时序偏好进行度量；然后通过构建优化模型求解时序权重，再结合证据信任度的概念，对证据源进行修正；最后利用Dempster组合规则对修正后的证据进行融合。数值算例表明，与没有考虑时间因素的融合方法相比，考虑决策者时序偏好的证据融合方法可以有效处理时域信息序列中的冲突信息，得到合理的融合结果；同时，所提方法充分考虑了时域证据序列的信任度和决策者的主观偏好，可以反映决策者主观因素对时域证据融合的影响，较好地体现了时域证据融合的动态性特点。     

基于证据距离和不确定度的冲突数据融合算法

Dempster-Shafer证据理论广泛应用于信息融合的许多领域。但是,当使用证据理论对高度冲突的数据进行融合时,此时会出现有违常理的结果。为了解决冲突数据融合的问题,提出了一种基于证据距离和不确定度的冲突数据融合方法。通过证据距离计算证据之间的相对距离,将证据分为两种类别：可信证据和不可信证据。再应用新提出的信度熵对证据不确定度进行度量,对每个证据分配相应的权重,再根据权重对每个证据的基本信度值进行修正,再运用Dempster融合规则对修正后的信度进行组合得到最终全局信度值。通过算例实验,与其他几种经典的数据融合算法进行对比,仿真结果证明算法能够有效地解决数据冲突的问题。     

基于加权证据理论的模糊信息融合目标识别

在异类多传感器信息融合目标识别中,不同传感器对系统提供的证据等级不同。为此,提出一种模糊信息融合目标识别方法。将各证据按证据权进行转化,用Dempster-Shafer(D-S)证据理论进行合成,利用模糊数学模型对传感器测量值和数据库中的数据进行建模,根据证据距离得到各证据的相互支持度,进而获得传感器对系统提供信息量的权重。分析结果表明,该方法具有较高的精度和可靠性。     

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.     

面向普适计算的扩展的证据理论方法

普适计算作为一种新型计算模式，从根本上改变人们对什么是计算的思考．由于它需对多源信息进行融合，因此该文作者认为它是一种包含融合计算的模式，能通过多层次、多视角的融合，为人们提供更方便的信任度高的访问信息和计算服务．基于普适计算应用的需要，该文讨论了扩展的证据理论方法，该方法采用可靠性因子评估多源证据觉察上下文信息；引入时效函数衡量多源证据的有效性与时间的关系，并将其组合到信任函数中，描述信任mass的时变规律；利用功率来度量多源证据觉察上下文信息间的相关程度，并通过去相关将其转化为相互独立的证据，扩展和完善了经典证据理论提供的方法，弥补了其不足之处，提高了不同应用场合下服务的质量(QoS)，确保了普适计算的服务宗旨．利用支持普适计算模式的智能空间中的场景，验证了扩展的有效性．     

Entailment for measure based belief structures

We discuss the Dempster–Shafer belief structure on finite universes and note its use for modeling variables that have both probabilistic uncertainty as well as imprecision. We note for these structures the probability that the variable lies in a subset cannot be precisely known but only be known to an interval value. We discuss methods for deducing this uncertainty interval. We next discuss the issue of entailment of belief structures, inferring the validity of additional belief model of a variable from an already established belief model of the variable. We next discuss a more general belief structure were the underling uncertainty rather tha0n being based on a probability distribution is based on a general measure type of uncertainty. We then extend the concept of entailment to the case where the belief structures are these more general measure based belief structures. In order to accomplish this we must extend the idea of containment from classic Dempster–Shafer belief structures to measure based belief structures.     

Evidence combination based on credibility and non-specificity

This paper addresses the combination of unreliable evidence sources which provide uncertain information in the form of basic probability assignment (BPA) functions. We proposed a novel evidence combination rule based on credibility and non-specificity of belief functions. Following a review of all existing non-specificity measures in evidence theory, a non-specificity measure for evidence theory is discussed. It is claimed that the non-specificity degree of a BPA is related to its ability of pointing to one and only one element. Based on the difference between the largest belief grades and other belief grades, a non-specificity measure is defined. Properties of the proposed non-specificity measure are put forward and proved mathematically. Illustrative examples are employed to show the properties of non-specificity measure. After providing a procedure for the evaluation of evidence credibility, we propose a novel evidence combination rule. Numerical example and application in target identification are applied to demonstrate the performance of our proposed evidence combination rule.     

A Clustering‐Based Evidence Reasoning Method

Aiming at the counterintuitive phenomena of the Dempster–Shafer method in combining the highly conflictive evidences, a combination method of evidences based on the clustering analysis is proposed in this paper. At first, the cause of conflicts is disclosed from the point of view of the internal and external contradiction. And then, a new similarity measure based on it is proposed by comprehensively considering the Pignistic distance and the sequence according to the size of the basic belief assignments over focal elements. This measure is used to calculate the commonality function of evidences to amend the evidence sources; Meanwhile, the Iterative Self‐organizing Data Analysis Techniques Algorithm (ISODATA) method based on the new measure is used for clustering according to the clustering characters of the original evidences. The Dempster rule is applied to combining all the evidences in each clustering into an evidential representative, and the reliability is calculated based on the commonality and the occurrence frequency of the evidences in the clustering. At last, Murphy's method is used to combine these evidential representatives of the different clusterings. The experimental results through a series of numeric examples show that the method proposed in this paper is more effective and superior to others.     

Representation and combination of uncertainty with belief functions and possibility measures

The theory of evidence proposed by G. Shafer is gaining more and more acceptance in the field of artificial intelligence, for the purpose of managing uncertainty in knowledge bases. One of the crucial problems is combining uncertain pieces of evidence stemming from several sources, whether rules or physical sensors. This paper examines the framework of belief functions in terms of expressive power for knowledge representation. It is recalled that probability theory and Zadeh's theory of possibility are mathematically encompassed by the theory of evidence, as far as the evaluation of belief is concerned. Empirical and axiomatic foundations of belief functions and possibility measures are investigated. Then the general problem of combining uncertain evidence is addressed, with focus on Dempster rule of combination. It is pointed out that this rule is not very well adapted to the pooling of conflicting information. Alternative rules are proposed to cope with this problem and deal with specific cases such as nonreliable sources, nonexhaustive sources, inconsistent sources, and dependent sources. It is also indicated that combination rules issued from fuzzy set and possibility theory look more flexible than Dempster rule because many variants exist, and their numerical stability seems to be better.     

A method for combining conflicting evidences with improved distance function and Tsallis entropy

For the sake of great ability of handling uncertain information, Dempster-Shafer evidence theory is extensively used in information fusion. Nevertheless, when there exists highly inconsistent evidences, using classical Dempster's combination rule may lead to counter-intuitive results. To address this issue, a new conflicting evidences combination method based on distance function and Tsallis entropy is proposed. Numerical examples are used to illustrate the feasibility and efficiency of the proposed method. Further, an fault diagnosis problem is used as an example to show the effectiveness and superiority of the proposed method. The proposed method outperforms other methods that the proposed method recognize the target by the probability 99.49%, which is higher than other methods.     

Extension of belief functions to infinite-valued events

We generalise belief functions to many-valued events which are represented by elements of Lindenbaum algebra of infinite-valued ?ukasiewicz propositional logic. Our approach is based on mass assignments used in the Dempster–Shafer theory of evidence. A generalised belief function is totally monotone and it has Choquet integral representation with respect to a unique belief measure on Boolean events.     

Combining belief functions taking into consideration error in judgement

ABSTRACT

Dempster–Shafer (D–S) evidence theory is very efficient and widely used mathematical tool for uncertain and imprecise information fusion for decision making. D–S rule is criticised by many researchers as it gives illogical and counterintuitive results especially when the series of evidence provided by various experts are in a high degree of conflict. Various attempts have been made and several alternatives proposed to this rule. In this paper, a new alternative is proposed which considers the possibility of an error made by experts while providing evidence, calculates the error and incorporates in the revised masses. The validity and efficiency of the proposed approach have been demonstrated with numerous examples and the results are compared with already existing methods.

Highlights

• An alternative method is proposed to handle the conflicting evidence.

• An Error In Judgement while gathering evidence is considered and incorporated before combining evidence.

• The method is simple and gives better and reasonable results than other previous methods when evidence conflicts

     

Evaluation method based on fuzzy relations between Dempster–Shafer belief structure

Many relations in the real world can be described by mathematical language. Fuzzy set theory can transform human language into mathematical language and use membership degree function to describe relations between events. Dempster–Shafer evidence theory provides basic probability assignment (BPA), which can describe the occurrence rate of attributes in basic events. Based on the known membership degree function and BPA distribution, a new evaluation method is proposed in this paper to analyze decision making. Given the relations among relevant events, which are expressed by BPA distribution and membership degree function, the relations among basic events and top event can be obtained. The Dempster's combination rule and pignistic probability transformation are used to transform BPA distribution into probability distribution. The belief measure is applied to deal with these fuzzy relations. Some numerical examples are given in this paper to illustrate the proposed evaluation methodology.     

Analyzing the combination of conflicting belief functions

We consider uncertain data which uncertainty is represented by belief functions and that must be combined. The result of the combination of the belief functions can be partially conflictual. Initially Shafer proposed Dempster’s rule of combination where the conflict is reallocated proportionally among the other masses. Then Zadeh presented an example where Dempster’s rule of combination produces unsatisfactory results. Several solutions were proposed: the TBM solution where masses are not renormalized and conflict is stored in the mass given to the empty set, Yager’s solution where the conflict is transferred to the universe and Dubois and Prade’s solution where the masses resulting from pairs of conflictual focal elements are transferred to the union of these subsets. Many other suggestions have then been made, creating a ‘jungle’ of combination rules. We discuss the nature of the combinations (conjunctive versus disjunctive, revision versus updating, static versus dynamic data fusion), argue about the need for a normalization, examine the possible origins of the conflicts, determine if a combination is justified and analyze many of the proposed solutions.