基于Lance距离和信度熵的冲突证据融合方法

doi:10.12305/j.issn.1001-506X.2022.02.29

Abstract

Abstract:

In view of the possible conflicts in the fusion of evidence in the D-S(Dempster-Shafer) evidence theory, a conflict evidence fusion method based on Lance distance and reliability entropy is proposed by considering the relationship between the evidence and their own characteristics. Firstly, Lance distance is used to measure the difference and conflict between evidences, and the credibility of evidence is determined by matrix form, then the information quantity of evidence is measured by calculating the credibility entropy, and the uncertainty of evidence is expressed.Secondly, the discount coefficient of the final fusion of evidence is measured by comprehensively considering the reliability and uncertainty of evidence, and the original evidence is corrected by the discount coefficient. Finally, Dempster synthesis rule is used for evidence fusion to get the final result. The results of example analysis show that the proposed method has faster convergence speed and more accurate and reliable fusion results than other methods.

Key words: D-S (Dempster-Shafer) evidence theory, conflict evidence, Lance distance, credibility entropy, credibility, uncertainty

CLC Number:

TP13
TJ06

Xuan WANG, Peng DI, Dongliang YIN. Conflict evidence fusion method based on Lance distance and credibility entropy[J]. Systems Engineering and Electronics, 2022, 44(2): 592-602.

Figures/Tables 10

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Fusion results of different evidence fusion methods when the original evidence source is normal"

融合方法	融合结果	第1次融合 m′₁(A_i)⊕m′₂(A_i) K=0.197 0	第2次融合 m′₁(A_i)⊕m′₂(A_i)⊕m′₃(A_i) K=0.600 7	第3次融合 m′₁(A_i)⊕m′₂(A_i)⊕m′₃(A_i)⊕m′₄(A_i) K=0.611 9	第4次融合 m′₁(A_i)⊕m′₂(A_i)⊕m′₃(A_i)⊕m′₄(A_i)⊕m′₅(A_i) K=0.650 7
Dempster合成规则	m(A₁) m(A₂) m(A₃) m(Θ)	0.986 3 0 0.013 7 0	0.991 7 0 0.008 3 0	0.999 9 0 0.000 1 0	1 0 0 0
文献[2]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.792 0 0 0.011 0 0.197 0	0.396 0 0 0.003 3 0.600 7	0.388 1 0 0 0.611 9	0.349 3 0 0 0.650 7
文献[7]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.893 0 0.000 6 0.022 9 0.083 5	0.659 1 0.024 2 0.062 2 0.254 5	0.675 5 0.019 4 0.045 9 0.259 2	0.661 3 0.020 2 0.042 8 0.275 7
文献[8]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.863 2 0.000 4 0.019 4 0.117 0	0.619 5 0.020 6 0.053 3 0.306 6	0.654 5 0.018 0 0.042 5 0.285 0	0.661 1 0.020 2 0.042 7 0.276 0
文献[9]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.863 2 0.000 4 0.019 4 0.117 0	0.627 4 0.017 7 0.050 6 0.304 3	0.661 1 0.014 3 0.038 2 0.286 4	0.669 1 0.016 7 0.038 3 0.275 9
文献[10]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.967 3 0.001 0 0.031 7 0	0.852 5 0.042 1 0.105 4 0	0.886 8 0.033 7 0.079 5 0	0.890 7 0.035 1 0.074 2 0
文献[11]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.967 3 0.001 0 0.031 7 0	0.870 0 0.036 4 0.093 6 0	0.904 8 0.028 2 0.067 0 0	0.906 6 0.030 0 0.063 4 0
文献[13]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.988 0 0 0.012 0 0	0.994 0 0.002 4 0.003 6 0	0.999 9 0 0.000 1 0	1 0 0 0
文献[15]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.999 4 0 0.000 6 0	0.998 4 0.000 6 0.001 0 0	0.996 4 0.000 2 0.003 4 0	0.999 6 0 0.000 4 0
文献[16]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.986 3 0 0.013 7 0	0.988 9 0.000 1 0.011 0 0	0.999 2 0 0.000 8 0	1 0 0 0
文献[18]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.986 3 0 0.013 7 0	0.991 7 0 0.008 3 0	0.999 9 0 0.000 1 0	1 0 0 0
文献[21]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.967 3 0.001 0 0.031 7 0	0.879 4 0.031 7 0.088 9 0	0.914 5 0.023 5 0.062 0 0	0.916 4 0.025 6 0.058 0 0
K-L距离^[19]	m(A₁) m(A₂) m(A₃) m(Θ)	0.512 4 0.025 2 0.098 2 0.364 2	0.536 5 0.024 6 0.082 5 0.356 4	0.523 6 0.016 5 0.060 6 0.399 3	0.579 9 0.021 6 0.056 1 0.342 3
Mahalanobis距离^[20]	m(A₁) m(A₂) m(A₃) m(Θ)	0.960 5 0.001 1 0.034 0 0.004 4	0.673 8 0.020 6 0.088 3 0.217 3	0.667 1 0.017 7 0.070 0 0.245 2	0.712 8 0.023 6 0.065 8 0.197 8
Lance距离^[22]	m(A₁) m(A₂) m(A₃) m(Θ)	0.987 8 0.000 6 0.011 6 0	0.944 6 0.015 9 0.039 5 0	0.968 8 0.009 7 0.023 5 0	0.972 9 0.008 6 0.018 5 0
本文提出的融合方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.952 9 0.010 4 0.036 6 0	0.991 4 0.001 1 0.007 5 0	0.998 4 0.000 1 0.001 5 0	0.999 6 0.000 1 0.000 3 0

Table 6

Fig.1

Table 7

Table 8

Fusion results of different evidence fusion methods when the original evidence source is conflict"

融合方法	融合结果	第1次融合 E₂ K=0.901 0	第2次融合 m′₁(A_i)⊕m′₂(A_i)⊕m′₃(A_i) K=0.970 3	第3次融合 m′₁(A_i)⊕m′₂(A_i)⊕m′₃(A_i)⊕m′₄(A_i) K=0.999 7	第4次融合 m′₁(A_i)⊕m′₂(A_i)⊕m′₃(A_i)⊕m′₄(A_i)⊕m′₅(A_i) K=1
Dempster合成规则	m(A₁) m(A₂) m(A₃) m(Θ)	0 0 1 0	0 0 1 0	0 0 1 0	0 0 1 0
文献[2]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0 0 0.099 0 0.901 0	0 0 0.029 7 0.970 3	0 0 0.000 3 0.999 7	0 0 0 1
文献[7]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.1647 0.001 9 0.298 4 0.535 0	0.223 2 0.033 5 0.251 3 0.492 0	0.319 2 0.029 5 0.188 1 0.463 2	0.378 1 0.031 1 0.167 1 0.423 7
文献[8]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.164 7 0.001 8 0.298 5 0.535 0	0.228 4 0.034 2 0.256 5 0.480 9	0.335 6 0.031 0 0.197 7 0.435 7	0.402 6 0.033 1 0.178 0 0.386 3
文献[9]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.164 7 0.001 8 0.298 5 0.535 0	0.254 2 0.045 6 0.223 1 0.477 1	0.403 0 0.035 6 0.123 7 0.437 7	0.4808 0.035 0 0.097 5 0.386 7
文献[10]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.405 5 0.004 5 0.590 0 0	0.452 8 0.067 9 0.479 3 0	0.594 8 0.055 0 0.350 2 0	0.595 1 0.055 0 0.349 9 0
文献[11]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.405 5 0.004 5 0.590 0 0	0.536 6 0.072 3 0.391 1 0	0.721 8 0.037 3 0.240 9 0	0.776 5 0.035 1 0.188 4 0
文献[13]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.454 5 0 0.545 5 0	0.590 9 0 0.409 1 0	0.991 8 0 0.008 2 0	0.999 2 0.000 4 0.000 4 0
文献[15]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.454 5 0 0.545 5 0	0.623 7 0 0.376 3 0	0.996 4 0.000 2 0.003 4 0	0.999 7 0 0.000 3 0
文献[16]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0 0 1 0	0.652 8 0.076 2 0.271 0 0	0.989 7 0 0.010 3 0	0.999 5 0 0.000 5 0
文献[18]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.017 9 0.000 2 0.981 9 0	0.952 8 0 0.047 2 0	0.999 9 0 0.000 1 0	1 0 0 0
文献[21]中方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.405 5 0.004 5 0.590 0 0	0.573 7 0.086 6 0.339 7 0	0.803 3 0.043 9 0.152 8 0	0.858 5 0.037 9 0.103 6 0
K-L距离^[19]	m(A₁) m(A₂) m(A₃) m(Θ)	0.405 5 0.004 5 0.590 0 0	0.350 2 0.067 7 0.285 0 0.297 1	0.444 6 0.052 3 0.175 4 0.327 7	0.524 9 0.050 3 0.136 6 0.282 2
Mahalanobis距离^[20]	m(A₁) m(A₂) m(A₃) m(Θ)	0.431 7 0.002 0 0.284 1 0.282 2	0.427 6 0.053 5 0.255 5 0.263 4	0.535 9 0.042 7 0.188 4 0.233 0	0.607 7 0.044 2 0.160 6 0.187 5
Lance距离^[22]	m(A₁) m(A₂) m(A₃) m(Θ)	0.517 1 0 0.482 9 0	0.603 6 0.006 8 0.389 6 0	0.875 3 0.010 5 0.114 2 0	0.920 6 0.008 1 0.071 3 0
本文提出的融合方法	m(A₁) m(A₂) m(A₃) m(Θ)	0.893 1 0.017 9 0.089 0 0	0.966 9 0.002 7 0.030 4 0	0.989 8 0.000 4 0.009 8 0	0.996 8 0.000 1 0.003 1 0

Table 8

Fig.2

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mass函数	m′(A₁)	m′(A₂)	m′(A₃)
m′₁	m_Avg(A₁)	m_Avg(A₂)	m_Avg(A₃)
m′₂	m_Avg(A₁)	m_Avg(A₂)	m_Avg(A₃)
$ \vdots $	$ \vdots $	$ \vdots $	$ \vdots $
m′_N	m_Avg(A₁)	m_Avg(A₂)	m_Avg(A₃)

证据融合	A₁	A₂	A₃
m′₁(A_k)⊕m′₂(A_k)	m′₁₂(A₁)	m′₁₂(A₂)	m′₁₂(A₃)
m′₁(A_k)⊕m′₂(A_k)⊕m′₃(A_k)	m′₁₂₃(A₁)	m′₁₂₃(A₂)	m′₁₂₃(A₃)
$ \vdots $	$ \vdots $	$ \vdots $	$ \vdots $
m′₁(A_k)⊕m′₂(A_k)⊕…⊕m′_N(A_k)	m_123…N(A₁)	m_123…N(A₂)	m_123…N(A₃)

mass函数	m′(A₁)	m′(A₂)	m′(A₃)
m′₁	0.768 8	0.080 5	0.150 7
m′₂	0.768 8	0.080 5	0.150 7
m′₃	0.768 8	0.080 5	0.150 7
m′₄	0.768 8	0.080 5	0.150 7
m′₅	0.768 8	0.080 5	0.150 7

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Conflict evidence fusion method based on Lance distance and credibility entropy

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证据	m(A₁)	m(A₂)	m(A₃)
E₁	0.90	0	0.10
E₂	0.88	0.01	0.11
E₃	0.50	0.20	0.30
E₄	0.98	0.01	0.01
E₅	0.90	0.05	0.05