Deqiang Han

A new distance-based total uncertainty measure in the theory of belief functions

A new total uncertainty measure in evidence theory is proposed.The new measure is directly defined in the evidential framework.The new measure is not a generalization of those in the probabilistic framework.The belief intervals and distance metric are used for the new measures design.The new measure has no drawbacks in traditional ones and has desired properties. The theory of belief functions is a very important and effective tool for uncertainty modeling and reasoning, where measures of uncertainty are very crucial for evaluating the degree of uncertainty in a body of evidence. Several uncertainty measures in the theory of belief functions have been proposed. However, existing measures are generalizations of measures in the probabilistic framework. The inconsistency between different frameworks causes limitations to existing measures. To avoid these limitations, in this paper, a new total uncertainty measure is proposed directly in the framework of belief functions theory without changing the theoretical frameworks. The average distance between the belief interval of each singleton and the most uncertain case is used to represent the total uncertainty degree of the given body of evidence. Numerical examples, simulations, applications and related analyses are provided to verify the rationality of our new measure.

Evidence Combination From an Evolutionary Game Theory Perspective

Dempster-Shafer evidence theory is a primary methodology for multisource information fusion because it is good at dealing with uncertain information. This theory provides a Dempsters rule of combination to synthesize multiple evidences from various information sources. However, in some cases, counter-intuitive results may be obtained based on that combination rule. Numerous new or improved methods have been proposed to suppress these counter-intuitive results based on perspectives, such as minimizing the information loss or deviation. Inspired by evolutionary game theory, this paper considers a biological and evolutionary perspective to study the combination of evidences. An evolutionary combination rule (ECR) is proposed to help find the most biologically supported proposition in a multievidence system. Within the proposed ECR, we develop a Jaccard matrix game to formalize the interaction between propositions in evidences, and utilize the replicator dynamics to mimick the evolution of propositions. Experimental results show that the proposed ECR can effectively suppress the counter-intuitive behaviors appeared in typical paradoxes of evidence theory, compared with many existing methods. Properties of the ECR, such as solutions stability and convergence, have been mathematically proved as well.

Discounted combination of unreliable evidence using degree of disagreement

Abstract When Dempster’s rule is used to implement a combination of evidence, all sources are considered equally reliable. However, in many real applications, all the sources of evidence may not have the same reliability. To resolve this problem, a number of methods for discounting unreliable sources of evidence have been proposed in which the estimation of the discounting (weighting) factors is crucial, especially when prior knowledge is unavailable. In this paper, we propose a new degree of disagreement through which discounting factors can be generated for discounting combinations of unreliable evidence. The new degree of disagreement is established using distance of evidence. It can be experimentally verified that our degree of disagreement describes the disagreements or differences among bodies of evidence well and that it can be effectively used in discounting combinations of unreliable evidence.

Evaluation of Probability Transformations of Belief Functions for Decision Making

The transformation of belief function into probability is one of the most important and common ways for decision making under the framework of evidence theory. In this paper, we focus on the evaluation of such probability transformations (PTs), which are crucial for their proper applications and the design of new ones. Shannon entropy or probabilistic information content (PIC) measure is traditionally used in evaluating PTs. The transformation having the lowest entropy or highest PIC is considered as the best one. This standpoint is questioned in this paper by comparing a PT based on uncertainty minimization with other available PTs. It shows experimentally that entropy or PIC is not comprehensive to evaluate a PT. To make a comprehensive evaluation, some new approaches are proposed by the joint use of PIC and the distance of evidence according to the value- and rank-based fusion. A pattern classification application oriented evaluation approach for PTs is also proposed. Some desired properties for PTs are also discussed. Experimental results and related analysis are provided to show the rationality of the new evaluation approaches.

A novel classifier based on shortest feature line segment

A new approach called shortest feature line segment (SFLS) is proposed to implement pattern classification in this paper, which can retain the ideas and advantages of nearest feature line (NFL) and at the same time can counteract the drawbacks of NFL. The proposed SFLS uses the length of the feature line segment satisfying given geometric relation with query point instead of the perpendicular distance defined in NFL. SFLS has clear geometric-theoretic foundation and is relatively simple. Experimental results on some artificial datasets and real-world datasets are provided, together with the comparisons between SFLS and other neighborhood-based classification methods, including nearest neighbor (NN), k-NN, NFL and some refined NFL methods, etc. It can be concluded that SFLS is a simple yet effective classification approach.

Sequential weighted combination for unreliable evidence based on evidence variance

Dempster-Shafer evidence theory is a powerful tool in uncertainty reasoning and decision-making. However counter-intuitive results can be encountered when unreliable bodies of evidence are combined by using Dempsters rule of combination in some cases. In this paper, a novel sequential evidence combination approach is proposed based on the weighted modification of bodies of evidence according to our proposed variances of evidence sequences. Experimental results show that the proposed approach is rational and effective. The proposed approach is a sequential evidence combination rule.Variance of evidence sequence is used to modify the bodies of evidence.The proposed approach can suppress counter-intuitive behaviors of Dempsters rule.

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.

Is entropy enough to evaluate the probability transformation approach of belief function

In Dempster-Shafer Theory (DST) of evidence and transferable belief model (TBM), the probability transformation is necessary and crucial for decision-making. The evaluation of the quality of the probability transformation is usually based on the entropy or the probabilistic information content (PIC) measures, which are questioned in this paper. Another alternative of probability transformation approach is proposed based on the uncertainty minimization to verify the rationality of the entropy or PIC as the evaluation criteria for the probability transformation. According to the experimental results based on the comparisons among different probability transformation approaches, the rationality of using entropy or Probabilistic Information Content (PIC) measures to evaluate probability transformation approaches is analyzed and discussed.

A Markov Random Field Model-based Fusion Approach to Segmentation of SAR and Optical Images

In this paper, a data fusion approach to the segmentation of SAR and optical images in Markov random field (MRF) framework is proposed. In the joint segmentation scheme based on an MRF model defined on a region adjacency graph (RAG), a fusion rule made on local features of source images is developed for appropriately measuring the feature saliency and incorporating the source reliability of each data source to weigh the source influence in the segmentation procedure. A specific scheme for segmentation of a set of Landsat Thematic Mapper (TM) images and a synthetic aperture radar (SAR) image is presented in detail. Comparative analysis of the proposed segmentation approach against several conventional segmentation approaches carried out on synthetic and real datasets confirms the effectiveness of the proposed approach.

New Distance Measures of Evidence Based on Belief Intervals

A distance or dissimilarity of evidence represents the degree of dissimilarity between bodies of evidence, which has been widely used in the applications based on belief functions theory. In this paper, new distance measures are proposed based on belief intervals [Bel, Pl]. For a basic belief assignment (BBA), the belief intervals of different focal elements are first calculated, respectively, which can be considered as interval numbers. Then, according to the distance of interval numbers, we can calculate the distance values between the corresponding belief intervals of the same focal elements in two given BBAs. Based on these distance values of belief intervals, new distance measures of evidence can be obtained using Euclidean and Chebyshev approaches, respectively. Some experiments and related analyses are provided to show the rationality and efficiency of the proposed measures.