On combination rule in Dempster–Shafer theory using OWA-based soft likelihood functions and its applications in environmental impact assessment

Dempster–Shafer theory (DST) was presented as an effective mathematical tool to represent uncertainty. Its significant innovation is to allow the allocation of the belief of mass to sets or intervals, and it becomes a valuable method in the field of decision making and evaluation when accurate information is not available or when knowledge is expressed subjectively by humans. A crucial research issue in DST is the combination of multi-sources of evidence. In this paper, a novel combination rule for Dempster–Shafer structures is developed based on ordered weighted average (OWA)-based soft likelihood functions proposed by Yager. First, the belief intervals, including the belief measures and plausibility measures, of all the hypotheses in the frame of discernment (FOD) are calculated. Second, the representative value of belief interval is defined based on golden rule introduced by Yager. Third, the soft likelihood value of each hypothesis is calculated based on the proposed OWA-based soft likelihood function for belief interval, which can be considered as the combined evidence. The final evaluation results can be employed for practical applications, such as decision making and evaluation. In addition, the improved evidence combination rule is presented which takes into account the weight of evidence. Several illustrative examples are conducted to manifest the use of the developed methods. Finally, an application for environmental impact assessment is given to demonstrate the usefulness of the developed combination rule in DST.     

直觉模糊集隶属度与非隶属度函数的确定方法

基于证据理论研究直觉模糊集隶属度和非隶属度函数的确定问题是一种新的思路.首先分析信任函数、似然函数与隶属度函数、非隶属度函数的互通性;然后给出广义基本概率分配(BPA)函数、广义信任函数和广义似然函数的定义;最后在这3个改进定义的基础上建立直觉模糊集隶属度函数、非隶属度函数模型,通过证明和实例验证了模型的正确性和有效性.     

A new probability transformation method based on a correlation coefficient of belief functions

The Dempster-Shafer evidence theory is widely used in many fields of information fusion because of its advantage in handling uncertain information. One of the key issues in this theory is how to make decision based on a basic probability assignment (BPA). Currently, a feasible scheme is transforming a BPA to a distribution of probabilities. However, little attention was paid to the correlation between BPA and probability distribution. In this paper, a novel method about the probability transformation based on a correlation coefficient of belief functions is proposed. The correlation coefficient is a new measurement, which can effectively measure the correlation between BPAs. The proposed method aims at maximizing the correlation coefficient between the given BPA and the transformed probability distribution. On the basis of this idea, the corresponding probability distribution can be obtained and could reflect the original information of the given BPA to the maximum extent. It is valid to consider that the proposed probability transformation method is reasonable and effective. Numerical examples are given to show the effectiveness of the proposed method.     

基于证据理论的覆盖决策信息系统的属性约简

覆盖决策信息系统的属性约简是粗糙集理论中的重要研究内容之一.文中讨论决策为覆盖的覆盖决策信息系统的属性约简,针对覆盖决策信息系统的一类约简,利用证据理论中的信任函数和似然函数给出约简的等价刻画.根据决策类的似然函数值定义覆盖的重要度和相对重要度,给出求解约简的算法,并以实例说明算法的有效性.     

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.     

证据理论在不确定性推理中的应用研究*

利用证据理论中的基本概率分配函数、信任函数和似然函数来描述和处理知识的不确定性。提出一个特殊的概率分配函数和新的组合规则,并以其为基础建立一个不确定性推理模型。实例证明该模型能有效地度量最终结论的不确定性。     

Unified uncertainty representation and quantification based on insufficient input data

Uncertainty quantification accuracy of system performance has an important influence on the results of reliability-based design optimization (RBDO). A new uncertain identification and quantification methodology is proposed considering the strong statistical variables, sparse variables, and interval variables simultaneously. Maximum likelihood function and Akaike information criterion (AIC) methods are used to identify the best-fitted distribution types and distribution parameters of sparse variables. The interval variables are represented with evidence theory. Finally, a unified uncertainty quantification framework considering the three types of uncertain design variables is put forward, and then the failure probability of system performance is quantified with belief and plausibility measures. The Kriging metamodel and random sampling method are used to reduce the computational complexity. Three examples are illustrated to verify the effectiveness of the proposed methodology.     

传感器网络节点数目算法的比较研究*

节点数目的确定问题直接影响着网络的运行成本和工作效率,是传感器网络研究中一个基本的研究课题。介绍并分析了基于瞬时和长时两种不同感应模型的节点计算算法,即基于调度的节点数量确定算法和基于暴露量的节点数量确定算法,给出了覆盖滑动窗口的概念,归纳出两种算法在精度、性能指标和应用范围等方面的差异,得出两种方法均能有效确定满足覆盖节点数目的门限值,只是各自的覆盖滑动窗口的尺寸有所不同的结论。     

基于信息无损视角的DS/AHP群决策方法

因参考点选择不恰当及折扣方式不合理,DS/AHP 群决策方法存在决策信息损失的问题。为此,基于由决策主体推理判断出的互斥方案组和七级标度陒对偏好信息,构建能够对所有决策主体在特定属性上进行偏好集成的主体信息融合模型。在此基础上参照传统方法中由知识矩阵向BPA函数转换的思想,以及利用Dempster组合规则进行信息融合的思想,提出能够综合集成所有属性上证据信息的方法步骤,并通过案例模拟验证该方法的科学有效性和应用可行性,其 Pignistic概率与标准结果之间的总差异程度较小。     

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.

     

无限论域中的粗糙近似空间与信任结构

在粗糙集理论中存在一对近似算子：下近似算子和上近似算子.而在Dempser-Shafer证据理论中有一对对偶的不确定性测度：信任函数与似然函数.集合的下近似和上近似可以看成是对该集合所表示信息的定性描述,而同一集合的信任测度和似然测度可以看成是对该集合的不确定性的定量刻画.针对各种复杂系统中不确定性知识的表示问题,介绍了无限论域中经典和模糊环境下信任结构及其导出的信任函数与似然函数的概念,建立了Dempser-Shafer证据理论中信任函数与似然函数和粗糙集理论中下近似与上近似之间的关系.阐述了由近似空间导出的下近似和上近似的概率生成一对对偶的信任函数和似然函数;反之,对于任何一个信任结构及其生成的信任函数与似然函数,必可以找到一个概率近似空间,使得由近似空间导出的下近似和上近似的概率分别恰好就是所给的信任函数和似然函数.最后,指出了主要理论成果在智能信息系统的知识表示和知识获取方面的潜在应用.     

不完备序信息系统的证据特征及属性约简

不完备有序信息系统粗糙集模型是经典粗糙集的扩展,利用优势关系代替等价关系能很好地处理含未知属性值和带有偏好关系的数据。研究了不完备序信息系统的证据特征,给出了不完备序上、下近似算子,并证明了二者分别与证据理论中的似然函数、信任函数相对应。进而提出了不完备序信息系统的[R]约简、信任约简以及似然约简的概念,探讨了它们之间的一致性,证明了[R]约简与信任约简是等价的,均是保持信任函数和的最小属性集合,得出了似然约简协调集必为[R]约简协调集的结论。     

一种新的区间直觉模糊集决策方法: 区间证据组合的角度

基于证据理论,提出一种新的区间直觉模糊集决策模型.首先采用区间直觉模糊集表示属性值,将区间直觉模糊数转换为区间BPA;然后利用基于区间数的组合规则进行融合;最后将融合后的区间BPA转换为经典BPA用于决策,可直接方便地实现多属性数据的融合.该模型的优点在于:简单直观,能更有效地反映原始信息的不确定度;通用性好,可以推广到其他区间直觉模糊集的应用领域.算例结果表明了所提出模型的有效性.     

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%.     

Attribute reduction based on evidence theory in incomplete decision systems

Attribute reduction is a basic issue in knowledge representation and data mining. This paper deals with attribute reduction in incomplete information systems and incomplete decision systems based on Dempster-Shafer theory of evidence. The concepts of plausibility reduct and belief reduct in incomplete information systems as well as relative plausibility reduct and relative belief reduct in incomplete decision systems are introduced. It is shown that in an incomplete information system an attribute set is a belief reduct if and only if it is a classical reduct and a plausibility consistent set must be a classical consistent set. In a consistent incomplete decision system, the concepts of relative reduct, relative plausibility reduct, and relative belief reduct are all equivalent. In an inconsistent incomplete decision system, an attribute set is a relative plausibility reduct if and only if it is a relative reduct, a plausibility consistent set must be a belief consistent set, and a belief consistent set is not a plausibility consistent set in general.     

基于正态云模型的基本概率指派生成方法及应用

基本概率指派（Basic probability assignment, BPA）生成 是应用D S证据理论的关键环节和第一步,而如何生成BPA仍然是一个有待解决的问题。本文 提出一种基于云模型的BPA生成方法,首先,采用逆向云发生器生成每类样本在某属性下的 正态云模型。其次,利用前件云发生器得到待测样本在该属性下对每类样本的确定度期望。 再次,给出一种正态云模型交叠度计算方法,用确定度最大类的正态云模型与其他种类的最 大交叠度作为对全集的信任度。最后,对确定度进行归一化得到待测样本的BPA。实验结果 验证了该方法的有效性,此外,在样本数据较少情况下也能有效生成BPA。     

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.     

Intuitionistic fuzzy evidential power aggregation operator and its application in multiple criteria decision-making

The theory of intuitionistic fuzzy sets (IFS) is widely used for dealing with vagueness and the Dempster--Shafer (D-S) evidence theory has a widespread use in multiple criteria decision-making problems under uncertain situation. However, there are many methods to aggregate intuitionistic fuzzy numbers (IFNs), but the aggregation operator to fuse basic probability assignment (BPA) is rare. Power average (P-A) operator, as a powerful operator, is useful and important in information fusion. Motivated by the idea of P-A power, in this paper, a new operator based on the IFS and D-S evidence theory is proposed, which is named as intuitionistic fuzzy evidential power average (IFEPA) aggregation operator. First, an IFN is converted into a BPA, and the uncertainty is measured in D-S evidence theory. Second, the difference between BPAs is measured by Jousselme distance and a satisfying support function is proposed to get the support degree between each other effectively. Then the IFEPA operator is used for aggregating the original IFN and make a more reasonable decision. The proposed method is objective and reasonable because it is completely driven by data once some parameters are required. At the same time, it is novel and interesting. Finally, an application of developed models to the ‘One Belt, One road’ investment decision-making problems is presented to illustrate the effectiveness and feasibility of the proposed operator.     

一种改进的多传感器敌我识别算法

在深入研究证据理论中基本可信度分配和信任函数的关系基础上,首次提出把信任函数作为基本可信度分配进行数据融合的思想.应用这一思想对多传感器的敌我识别提出了一种改进的融合算法,仿真结果表明:该算法更具有可分析性,且计算复杂度也大大降低.     

随机覆盖目标信息系统的属性约简

引入随机覆盖目标信息系统的概念,以证据理论中的信任测度和似然测度为基本工具,研究了协调随机覆盖目标信息系统的属性约简和不协调随机覆盖目标信息系统的正域约简问题,最后给出实例验证了约简方法的有效性。