王保云, 王桂林, 王婷, 杨昆. 基于矩阵奇异值分解的证据冲突度量算法[J]. 云南大学学报(自然科学版), 2015, 37(1): 43-51. doi: 10.7540/j.ynu.20140212
引用本文: 王保云, 王桂林, 王婷, 杨昆. 基于矩阵奇异值分解的证据冲突度量算法[J]. 云南大学学报(自然科学版), 2015, 37(1): 43-51. doi: 10.7540/j.ynu.20140212
WANG Bao-yun, WANG Gui-lin, WANG Ting, YANG Kun. Evidence conflict measure based on singular value decomposition of matrix[J]. Journal of Yunnan University: Natural Sciences Edition, 2015, 37(1): 43-51. DOI: 10.7540/j.ynu.20140212
Citation: WANG Bao-yun, WANG Gui-lin, WANG Ting, YANG Kun. Evidence conflict measure based on singular value decomposition of matrix[J]. Journal of Yunnan University: Natural Sciences Edition, 2015, 37(1): 43-51. DOI: 10.7540/j.ynu.20140212

基于矩阵奇异值分解的证据冲突度量算法

Evidence conflict measure based on singular value decomposition of matrix

  • 摘要: 针对证据理论中证据冲突度量这一关键问题,提出了基于矩阵奇异值分解的证据冲突度量算法.首先将证据的BPA向量投影到单位圆上,然后运用投影后证据向量的BPA矩阵和焦元关联矩阵构造归一化BPA矩阵,接着对其进行奇异值分解,最后根据奇异值定义证据的最大干扰分量与主分量,并将二者比值作为冲突度量.通过对Zadeh悖论扩展形式、完全冲突证据和焦元为嵌套子集等多种情况进行对比实验,验证了本文算法是较为理想的证据冲突度量方式,能够正确预测证据集的冲突程度.

     

    Abstract: The conflict measure of evidences is the key issue for the evidence theory.A new method for conflict measure based on singular value decomposition(SVD) of matrix was proposed in this paper.The new method firstly normalize the BPA matrix of evidences by a projection operation.Then the SVD algorithm was used on the normalized BPA matrix to capture the largest and the second largest singular values.The largest singular value meant the main combining direction and second largest one meant the strongest direction of conflict.So the ratio of the largest singular value and the second largest one was used to measure the conflict of evidences.Experiments of the Zadeh paradox,completely conflict evidences set,and nesting sequence of focal elements showed that the new method could measure the conflict of evidences with a good performance.

     

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