On The Fusion Of Dependent Evidence

D-S evidence theory is becoming an increasingly important tool in the information fusion system due to its ?exibility in representing and handling uncertainty information.However, the classical evidence theory assumes that evidence are independent, which is unrealistic. Ignore the dependence among evidences may cause unreasonable result or even lead to wrong decision, which limits the applications and further development of evidence theory. This dissertation centers on the the modeling of dependence relationship, the dependence degree and the combination of dependent evidences. Based on these, we establish a systematic framework of handling dependent evidences and also work on the relationship between dependence and con?ict of the evidence. The main contributions and innovative points are list as follows:Propose the generalized Dempster’s combination rule, which can deal with the dependent evidence with “If-then” logical relationship effectively. First, we draw lessons from the classical probability theory about the conditional probability, and de?ne the conditional basic belief assignment, the joint basic belief assignment etc. between different information sources for one speci?c object. Then, a new generalized Dempster’s rule is proposed. Also its procedure and the extent of its application are discussed. The examples indicate that, compared with classical Dempster’s rule and the combination rule based on Hint theory, the proposed method can better represent the uncertainty information and can realize the mapping from point to distribution, and thus can deal with dependent evidence more effectively.Propose a new combination method based on the “Common evidence model”. It takes the relative importance of the common evidence into consideration in the updating process, which extend the classical “Common evidence model”. First, we discuss about the shortcomings of the traditional model. Then, a new combination model is proposed: calculate the relative importance degree of the independent evidence, and get the discount BBA of the common evidence with respect to each dependent evidence; use the “decombination” method to obtain the discount BBA of the independent evidence; Finally, combine all BBAs by using the weighted combination method. A numerical example reveals that after considering the relative importance of each part,the accuracy of the result has been improved.By analyzing the mechanism of dependence among evidence, we creatively divide the dependence into two types, i.e., internal dependence and external dependence.Also, with consideration of the importance and reliability of evidence, we propose a systematical framework of the discount model, which can be used for dealing with complicated situation under uncertainty. According to different practical situations,researches are done from statistics and expert evaluation point of view, respectively.First, we propose a new statistic-parameters based discount model under the situations when a fair amount of data samples are available. The Iris recognition problem is applied to show the robustness and correctness of the proposed method. Second, we propose another new discount model based on the comprehensive evaluation method,including the ANP and the new weighted degree-of-freedom method, which is used for situations of lacking data or qualitative data. The transportation project selection problem indicates the practicability of the comprehensive evaluation method. Moreover, we extend the new weighted degree-of-freedom method under uncertainty and successfully applied it to human error probability evaluation in nuclear power plant.Explore the relationships between dependent evidence and con?ict evidence, creatively solve the combination problem of con?ict evidence from the perspective of dependence. First, discuss four possible relationship between dependent and con?ict. Then, establish a new Gaussian dependence model based combination method for con?ict evidence. This can be used in the group decision making under open environment. The method de?ne three types of dependence degree and its related parameter of Gaussian distribution. Then, reconstruct the BBA based on former information, and combine the BBAs by Dempster’s combination rule. Finally, some examples and the application in FMEA RPN problem shows the effectiveness of the proposed method.