非单点证据体数据融合的Dempster组合规则适用性评价方法

针对待融合的证据体包含基本概率分配值相差较大的非单点证据时,基于pignistic距离的Dempster组合规则适用性评价方法判定结果存在模糊性甚至不准确的问题,提出了一种表示证据体之间关联性的改进pignistic距离,并将改进的pignistic距离与经典冲突系数相结合,提出了对Dempster组合规则适用性评价的新方法。在新方法中,定义了一种新的证据体冲突衡量系数用于判定Dempster规则的适用性。当经典冲突系数为0时,新系数与改进pignistic距离一致;当经典冲突系数不为0时,新系数与改进pignistic距离和经典冲突系数之和的平均值一致。算例分析的结果表明,与基于pignistic距离的Dempster规则适用性评价方法相比,新的基于改进pignistic距离的Dempster组合规则适用性评价方法有较好的适用性和合理性。     

基于冲突系数和pignistic概率距离的改进证据组合方法

针对单一使用冲突系数描述证据冲突存在的不足,从冲突系数和pignistic概率距离2个组合元素的角度出发,在冲突系数和pignistic概率距离形成的平面直角坐标系中,通过计算证据源对应的点到直线的距离表征证据之间的冲突,将冲突信息转换为支持信息,通过权重系数修正证据源,采用Dempster组合规则合成.通过算例分析和对比,证明了改进证据组合方法的可行性和优越性.     

Credit card fraud detection: A fusion approach using Dempster–Shafer theory and Bayesian learning

We propose a novel approach for credit card fraud detection, which combines evidences from current as well as past behavior. The fraud detection system (FDS) consists of four components, namely, rule-based filter, Dempster–Shafer adder, transaction history database and Bayesian learner. In the rule-based component, we determine the suspicion level of each incoming transaction based on the extent of its deviation from good pattern. Dempster–Shafer’s theory is used to combine multiple such evidences and an initial belief is computed. The transaction is classified as normal, abnormal or suspicious depending on this initial belief. Once a transaction is found to be suspicious, belief is further strengthened or weakened according to its similarity with fraudulent or genuine transaction history using Bayesian learning. Extensive simulation with stochastic models shows that fusion of different evidences has a very high positive impact on the performance of a credit card fraud detection system as compared to other methods.     

Some notes on betting commitment distance in evidence theory

The distance of evidence, which represents the degree of dissimilarity between bodies of evidence, has attracted more and more interest and has found extensive uses in many realms. In this paper some notes on a widely used distance of evidence, i.e., betting commitment distance, are provided, including the arguments on the rationality of its definition, some misuses and some counter-intuitive behaviors of betting commitment distance. Several numerical examples are also provided to support and verify our arguments.     

An expectation operator for belief functions in the Dempster–Shafer theory*

ABSTRACT

The main contribution of this paper is a new definition of expected value of belief functions in the Dempster–Shafer (D–S) theory of evidence. Our definition shares many of the properties of the expectation operator in probability theory. Also, for Bayesian belief functions, our definition provides the same expected value as the probabilistic expectation operator. A traditional method of computing expected of real-valued functions is to first transform a D–S belief function to a corresponding probability mass function, and then use the expectation operator for probability mass functions. Transforming a belief function to a probability function involves loss of information. Our expectation operator works directly with D–S belief functions. Another definition is using Choquet integration, which assumes belief functions are credal sets, i.e. convex sets of probability mass functions. Credal sets semantics are incompatible with Dempster's combination rule, the center-piece of the D–S theory. In general, our definition provides different expected values than, e.g. if we use probabilistic expectation using the pignistic transform or the plausibility transform of a belief function. Using our definition of expectation, we provide new definitions of variance, covariance, correlation, and other higher moments and describe their properties.     

多粒度模糊粗糙集的表示与相应的信任结构

利用多粒度粗糙集的上、下近似及其性质,结合模糊集的分解定理,研究多粒度模糊粗糙集的上、下近似的表示及性质,根据多粒度模糊粗糙集的上、下近似构造信任函数与似然函数。     

D-S证据理论在审计证据融合中的应用研究

古典概率难以解释审计判断的不确定性,而D-S证据理论是进行不确定性推理的有效方法,因此应用D-S证据理论进行审计证据融合的研究。针对审计证据的组合问题,提出了基于三角形模糊隶属度函数的基本概率分配函数计算方法,给出了证据组合结果的判决规则,并通过实例验证了该方法的有效性。     

Techniques for Computing Fitness of Use (FoU) for Time Series Datasets with Applications in the Geospatial Domain

Time series data are widely used in many applications including critical decision support systems. The goodness of the dataset, called the Fitness of Use (FoU), used in the analysis has direct bearing on the quality of the information and knowledge generated and hence on the quality of the decisions based on them. Unlike traditional quality of data which is independent of the application in which it is used, FoU is a function of the application. As the use of geospatial time series datasets increase in many critical applications, it is important to develop formal methodologies to compute their FoU and propagate it to the derived information, knowledge and decisions. In this paper we propose a formal framework to compute the FoU of time series datasets. We present three different techniques using the Dempster–Shafer belief theory framework as the foundation. These three approaches investigate the FoU by focusing on three aspects of data: data attributes, data stability, and impact of gap periods, respectively. The effectiveness of each approach is shown using an application in hydrological datasets that measure streamflow. While we use hydrological information analysis as our application domain in this research, the techniques can be used in many other domains as well.

基于改进权重的D-S证据理论的动态负载平衡算法

针对大型网络游戏中易出现的服务器集群负载不均衡的问题,提出基于改进权重的D-S（Dempster和Shafer）证据理论的负载平衡判别策略。首先,根据D-S证据理论,将影响服务器性能的多因素作为判据,利用历史数据与阈值大小的比较规则计算动态权重,再依据动态权重与原始信度的关系建立基本信任函数;然后,计算不同判据对应结果的信任函数,使用证据合成规则作深层融合;最后分析合成结果,最终推断服务器是否超载。模拟实验结果表明,与基于负反馈机制的动态均衡算法相比,所提算法的准确率更高,更符合真实情况;且所提算法的运行时间明显少于基于负反馈机制的动态均衡算法以及加权循环算法。实验结果表明,新算法有效缩短了运行判断的延迟,能够根据历史参数对当前服务器负载情况快速作出推断,且决策结果可信度高,更符合实际情况。     

A comparison of three uncertainty calculi for building sonar-based occupancy grids

In this paper, we describe and compare three different uncertainty calculi techniques to build occupancy grids of an unknown environment using sensory information provided by a ring of ultrasonic range-finders. These techniques are based on Bayesian theory, Dempster–Shafer theory of evidence, and fuzzy set theory. Several sensor models are presented to handle uncertainty according to the selected building procedure. Experimental examples of occupancy grids, built from real data recorded by two different mobile robots in office-like environment, are presented to perform a comparison among the proposed calculi techniques. Probabilistic and evidence theoretic methods are more accurate in structured environments, while in cases of multiple reflections only the possibilistic approach provides correct results.     

Credibility decay model in temporal evidence combination

Data fusion in time domain is sequential and dynamic. Methods to deal with evidence conflict in spatial domain may not suitable in temporal domain. It is significant to determine the dynamic credibility of evidence in time domain. The Markovian requirement of time domain fusion is analyzed based on Dempster's combination rule and evidence discount theory. And the credibility decay model is presented to get the dynamic evidence credibility. Then the evidence is discounted by dynamic discount factor. It's illustrated that such model can satisfied the requirement of data fusion in time domain. Proper and solid decision can be made by this approach.     

A novel fuzzy evidential reasoning paradigm for data fusion with applications in image processing

This paper presents a novel data fusion paradigm based on fuzzy evidential reasoning. A new fuzzy evidence structure model is first introduced to formulate probabilistic evidence and fuzzy evidence in a unified framework. A generalized Dempster’s rule is then utilized to combine fuzzy evidence structures associated with multiple information sources. Finally, an effective decision rule is developed to take into account uncertainty, quantified by Shannon entropy and fuzzy entropy, of probabilistic evidence and fuzzy evidence, to deal with conflict and to achieve robust decisions. To demonstrate the effectiveness of the proposed paradigm, we apply it to classifying synthetic images and segmenting multi-modality human brain MR images. It is concluded that the proposed paradigm outperforms both the traditional Dempster–Shafer evidence theory based approach and the fuzzy reasoning based approach