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摘要:
为有效融合多源数据以充分利用多源数据信息，针对只包含单子集焦元证据的多源数据融合时存在证据冲突的问题，提出了面向单子集焦元冲突证据的融合方法。综合考虑证据间的关联性和证据本身的不确定性2个方面，引入夹角余弦度量证据间的冲突程度来修正冲突系数和Jousselme距离的不足，利用冲突系数和信息熵的组合构造判断规则对证据进行分组，结合证据的支持度和可信度共同修正证据，进而实现单子集焦元冲突证据的有效融合。以4种典型冲突悖论为数值案例，验证了所提方法有效可行，且融合性能优于传统证据融合方法。
Abstract:To effectively fuse multi-source data and fully utilize multi-source data information, a conflict evidence fusion method for single-subset focal elements was proposed in response to evidence conflicts in fusion of multi-source data that only contains single-subset focal element evidence. Comprehensively considering the correlation between evidence and the uncertainty of the evidence itself, this study introduced the cosine of the included angle to measure the degree of conflict between evidence for correcting the deficiency of conflict coefficient and Jousselme distance. The combination of conflict coefficient and information entropy was used to construct judgment rules for evidence grouping, and then the evidence was modified with its support and credibility, so as to achieve effective fusion of single-subset focal element conflict evidence. With four typical conflict paradoxes as numerical cases, the proposed method is verified to be effective and feasible, and its fusion performance is better than that of the traditional evidence fusion method.
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图 1 单子集焦元冲突证据融合方法流程
Figure 1. Flow chart of conflict evidence fusion method for single-subset focal elements
表 1 不同组证据的BPA
Table 1. BPA of different sets of evidence
组号 BPA 1 $\begin{gathered} {m_1}({A_1}) = {m_1}({A_2}) = 0.5 \\ {m_2}({A_1}) = {m_2}({A_2}) = 0.5 \\ \end{gathered} $ 2 $\begin{gathered} {m_1}({A_1}) = {m_1}({A_2}) = 0.5 \\ {m_2}({A_3}) = {m_2}({A_4}) = 0.5 \\ \end{gathered} $ 3 $\begin{gathered} {m_1}({A_1}) = {m_1}({A_2}) = {m_1}({A_3}) = {1}/{3} \\ {m_2}({A_4}) = {m_2}({A_5}) = {m_2}({A_6}) = {1}/{3} \\ \end{gathered} $ 
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表 2 4种典型高冲突证据融合结果
Table 2. Fusion results of four kinds of typical high conflict evidence
悖论
类型融合方法 基本概率赋值 目标
命题命题A 命题B 命题C 识别框架$\varTheta $ 完全冲
突悖论Yager[4] 0 0 0 1 $\varTheta $ Murphy[14] 0.8375 0.1625 0 0 A Deng[15] 0.9986 0.0014 0 0 A Chen[17] 0.9986 0.0014 0 0 A Ye[19] 0.9250 0.0750 0 0 A Yuan[23] 0.9986 0.0014 0 0 A IDS 0.9999 0.0001 0 0 A 0信任
悖论DS[2] 0 0.6316 0.3684 0 B Yager[4] 0 0.0180 0.0105 0.9895 $\varTheta $ Murphy[14] 0.3500 0.5224 0.1276 0 B Deng[15] 0.5816 0.2439 0.1745 0 A Chen[17] 0.6195 0.2010 0.1795 0 A Ye[19] 0.6220 0.1974 0.1805 0 A Yuan[23] 0.7319 0.0790 0.1891 0 A IDS 0.7319 0.0790 0.1891 0 A 1信任
悖论DS[2] 0 1 0 0 B Yager[4] 0 0.01 0 1 $\varTheta $ Murphy[14] 0.4880 0.0241 0.4880 0 A/C Deng[15] 0.4880 0.0241 0.4880 0 A/C Chen[17] 0.4880 0.0241 0.4880 0 A/C Ye[19] 0.4880 0.0241 0.4880 0 A/C Yuan[23] 0.4880 0.0241 0.4880 0 A/C IDS 0.4880 0.0241 0.4880 0 A/C 高冲突
悖论DS[2] 0 0.9153 0.0847 0 B Yager[4] 0 0.0002 0 1 $\varTheta $ Murphy[14] 0.8389 0.1502 0.0099 0.0010 A Deng[15] 0.9524 0.0389 0.0078 0.0009 A Chen[17] 0.9623 0.0289 0.0078 0.0010 A Ye[19] 0.9509 0.0405 0.0077 0.0009 A Yuan[23] 0.9610 0.0268 0.0105 0.0017 A IDS 0.9959 0.0023 0.0017 0.0001 A
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