D-S证据理论中冲突证据的研究及其应用

发布时间：2019-03-20 07:20

【摘要】：D-S证据理论对不确定性信息的处理有很大的灵活性,具有广泛的应用领域。但是,D-S证据理论在实际应用中,常常会面临各种不一致性或冲突的证据,对这些冲突证据的定量度量及合成引起了大量学者的研究。本文针对D-S证据理论在冲突证据的度量、冲突证据的合成及基本可信度分配函数的构造等方面进行了深入研究,主要工作如下:(1)针对传统的冲突度量和Jousselme距离度量出现冲突误判的问题,提出了一种相似系数和Jaccard系数矩阵的证据冲突度量方法。该方法通过计算证据之间的相似系数,利用Jaccard系数矩阵将相似系数转化为证据的冲突程度。理论证明和数值计算表明该方法可以有效的表示证据间的冲突程度。通过典型的算例将本文的方法与其他方法进行对比,表明该方法可以有效的度量证据间的冲突程度。(2)针对使用冲突系数辨识证据冲突存在的不足,将Pignistic概率距离转换为证据的可信度,再将证据的可信度和虚假度结合起来,构造一个新的修正系数,然后利用新的修正系数来折扣基本可信度分配函数。利用D-S证据组合规则对修正后的证据进行合成。数值算例分析的结果表明,改进后的证据组合方法得到的结果具有收敛速度快和鲁棒性好的特点,同时保持了D-S组合规则的优良性质。(3)证据理论应用中的关键问题是基本可信度分配函数的构造,但是现在仍然没有一个统一的构造基本可信度分配函数的方法。利用区间数距离来表示样本属性之间的差异性,在此基础上归一化区间数距离得到基本可信度分配函数。通过Iris Data的分类实验验证了该方法的有效性。
[Abstract]:DES evidence theory has great flexibility in the processing of uncertain information and has a wide range of applications. However, in practical applications, DES evidence theory often faces a variety of inconsistent or conflicting evidence, the quantitative measurement and composition of these conflicting evidence has caused a large number of scholars to study. This paper makes an in-depth study on the measurement of conflicting evidence, the composition of conflicting evidence and the construction of basic confidence distribution function in DES evidence theory. The main work is as follows: (1) aiming at the problem of conflict misjudgment in traditional conflict measurement and Jousselme distance metric, a method of evidence conflict measurement based on similarity coefficient and Jaccard coefficient matrix is proposed. In this method, the similarity coefficient between evidence is calculated, and the similarity coefficient is transformed into the conflict degree of evidence by using the Jaccard coefficient matrix. Theoretical proof and numerical calculation show that this method can effectively represent the degree of conflict between the evidence. A typical example is given to compare the proposed method with other methods, and it is shown that the proposed method can effectively measure the degree of conflict between evidence. (2) in view of the shortcomings of using conflict coefficient to identify evidence conflicts, the proposed method can be used to measure the conflict degree of evidence effectively. The Pignistic probability distance is converted into the credibility of evidence, and then the credibility and false degree of evidence are combined to construct a new correction coefficient. Then the basic confidence distribution function is discounted by using the new correction coefficient. The modified evidence is synthesized by the combination rule of DES evidence. The results of numerical examples show that the results obtained by the improved evidence combination method have the characteristics of fast convergence speed and good robustness. (3) the key problem in the application of evidence theory is the construction of basic confidence distribution function, but there is still no unified method to construct the basic confidence distribution function. The interval number distance is used to represent the difference between the attributes of the sample. On this basis, the basic confidence allocation function is obtained by normalizing the interval number distance. The effectiveness of the proposed method is verified by Iris Data classification experiments.
【学位授予单位】：淮北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP202

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