Journal of Systems Engineering and Electronics ›› 2024, Vol. 35 ›› Issue (6): 1454-1468.doi: 10.23919/JSEE.2024.000101
• SYSTEMS ENGINEERING • Previous Articles
Xiaobo DUAN(), Qiucen FAN(
), Wenhao BI(
), An ZHANG(
)
Received:
2023-05-05
Online:
2024-12-18
Published:
2025-01-14
Contact:
Wenhao BI
E-mail:duanxiaobo@mail.nwpu.edu.cn;fanqc1006@mail.nwpu.edu.cn;biwenhao@nwpu.edu.cn;zhangan@nwpu.edu.cn
About author:
Supported by:
Xiaobo DUAN, Qiucen FAN, Wenhao BI, An ZHANG. Belief exponential divergence for D-S evidence theory and its application in multi-source information fusion[J]. Journal of Systems Engineering and Electronics, 2024, 35(6): 1454-1468.
Table 1
Comparisons of conflict extent in Example 2"
Λ | BED | k | 1-sim | ECC | RB | |
0.682 4 | 0.050 0 | 0.785 8 | 0.741 8 | 0.929 7 | 0.717 0 | |
0.359 2 | 0.050 0 | 0.686 6 | 0.528 5 | 0.795 9 | 0.633 0 | |
0.211 6 | 0.050 0 | 0.570 5 | 0.349 3 | 0.601 8 | 0.512 0 | |
0.109 0 | 0.050 0 | 0.423 7 | 0.196 6 | 0.354 2 | 0.342 0 | |
0.019 1 | 0.050 0 | 0.132 3 | 0.037 6 | 0.018 6 | 0.274 0 | |
0.108 7 | 0.050 0 | 0.388 4 | 0.196 0 | 0.300 9 | 0.195 0 | |
0.209 5 | 0.050 0 | 0.502 9 | 0.346 5 | 0.482 7 | 0.589 0 | |
0.264 8 | 0.050 0 | 0.570 5 | 0.418 7 | 0.595 2 | 0.613 0 | |
0.311 4 | 0.050 0 | 0.618 7 | 0.474 9 | 0.673 7 | 0.634 0 | |
0.351 2 | 0.050 0 | 0.655 4 | 0.519 8 | 0.730 7 | 0.653 0 | |
0.385 6 | 0.050 0 | 0.684 4 | 0.556 6 | 0.773 6 | 0.670 0 | |
0.415 6 | 0.050 0 | 0.708 2 | 0.587 2 | 0.806 5 | 0.686 0 | |
0.442 1 | 0.050 0 | 0.728 1 | 0.613 1 | 0.832 5 | 0.702 0 | |
0.465 7 | 0.050 0 | 0.745 1 | 0.635 3 | 0.853 4 | 0.716 0 | |
0.486 5 | 0.050 0 | 0.759 9 | 0.654 6 | 0.870 4 | 0.730 0 | |
0.505 4 | 0.050 0 | 0.773 0 | 0.671 4 | 0.884 4 | 0.743 0 | |
0.522 4 | 0.050 0 | 0.784 6 | 0.686 3 | 0.896 2 | 0.756 0 | |
0.537 9 | 0.050 0 | 0.795 1 | 0.699 5 | 0.906 1 | 0.768 0 | |
0.552 0 | 0.050 0 | 0.804 6 | 0.711 3 | 0.914 6 | 0.780 0 | |
0.564 9 | 0.050 0 | 0.813 3 | 0722 0 | 0.923 7 | 0.792 0 |
Table 2
Outcomes by different approaches in Example 3"
Approach | Mass |
Dempster’s rule [ | |
Murphy’s method [ | |
Zhu’s method [ | |
Xiao’s method [ | |
Proposed approach | |
Table 3
Outcomes by different approaches in Example 4"
Approach | Mass |
Dempster’s rule [ | |
Murphy’s method [ | |
Zhu’s method [ | |
Xiao’s method [ | |
Proposed approach | |
Table 4
Outcomes by different approaches in Example 5"
Approach | Mass |
Dempster’s rule [ | invalid |
Murphy’s method [ | |
Zhu’s method [ | |
Xiao’s method [ | |
Proposed approach | |
Table 5
Final combination outcomes obtained by different fusion methods"
Fusion method | m(T) | m(W) | m(R) | m(T,R) | Target |
Dempster’s rule [ | 0.865 7 | 0.016 8 | 0.116 7 | 0.000 7 | T |
Murphy’s method [ | 0.969 4 | 0.017 5 | 0.011 0 | 0.002 1 | T |
Deng’s method [ | 0.988 5 | 0.001 3 | 0.007 9 | 0.002 3 | T |
Gao’s method [ | 0.988 7 | 0.001 9 | 0.006 9 | 0.002 5 | T |
Xiao’s method [ | 0.988 8 | 0.001 5 | 0.007 3 | 0.002 4 | T |
Proposed approach | 0.991 1 | 0.000 2 | 0.006 3 | 0.002 4 | T |
Table 6
Fusion results through different methods"
Approach | Mass | |||
Dempster’s rule [ | 0.000 0 | 0.000 0 | 0.000 0 | |
0.991 6 | 0.996 8 | 0.998 8 | ||
0.008 4 | 0.003 2 | 0.001 2 | ||
0.000 0 | 0.000 0 | 0.000 0 | ||
0.000 0 | 0.000 0 | 0.000 0 | ||
0.000 0 | 0.000 0 | 0.000 0 | ||
0.000 0 | 0.000 0 | 0.000 0 | ||
Murphy’s method [ | 0.065 5 | 0.211 2 | 0.442 2 | |
0.882 8 | 0.774 9 | 0.554 6 | ||
0.050 5 | 0.013 9 | 0.003 2 | ||
0.000 6 | 8×10−6 | 8×10−8 | ||
4×10−5 | 2×10−7 | 5×10−10 | ||
0.000 5 | 8×10−6 | 6×10−7 | ||
1×10−5 | 3×10−8 | 3×10−11 | ||
Deng’s method [ | 0.065 5 | 0.312 9 | 0.730 1 | |
0.882 8 | 0.653 4 | 0.265 2 | ||
0.050 5 | 0.024 7 | 0.004 7 | ||
0.000 6 | 2×10−5 | 1×10−7 | ||
4×10−5 | 4×10−7 | 7×10−10 | ||
0.000 5 | 2×10−5 | 9×10−7 | ||
1×10−5 | 5×10−8 | 5×10−11 | ||
Gao’s method [ | 0.065 5 | 0.319 0 | 0.797 6 | |
0.882 8 | 0.660 0 | 0.199 0 | ||
0.050 5 | 0.021 0 | 0.003 4 | ||
0.000 6 | 1×10−5 | 5×10−8 | ||
4×10−5 | 3×10−7 | 3×10−10 | ||
0.000 5 | 1×10−5 | 6×10−7 | ||
1×10−5 | 4×10−8 | 2×10−11 | ||
Zhu’s method [ | 0.274 0 | 0.535 3 | 0.825 5 | |
0.521 0 | 0.371 7 | 0.155 6 | ||
0.200 3 | 0.092 8 | 0.018 9 | ||
0.002 5 | 9×10−5 | 1×10−6 | ||
0.000 2 | 2×10−6 | 6×10−9 | ||
0.002 0 | 8×10−5 | 3×10−6 | ||
5×10−5 | 3×10−7 | 5×10−10 | ||
Proposed approach | 0.274 0 | 0.533 8 | 0.836 8 | |
0.521 0 | 0.367 3 | 0.145 3 | ||
0.200 3 | 0.093 8 | 0.017 9 | ||
0.002 5 | 0.000 1 | 1×10−6 | ||
0.000 2 | 2×10−5 | 6×10−9 | ||
0.002 0 | 8×10−5 | 3×10−6 | ||
5×10−5 | 3×10−7 | 4×10−12 |
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