基于幂Pignistic概率距离的加权证据组合方法

doi:10.11959/j.issn.1000-436x.2018003

Abstract

Abstract:

To deal with the shortcomings encountered when using the existing similarity/dissimilarity measures to quantify evidence conflict,a new dissimilarity measure called power-Pignistic probability distance was defined.Furthermore,a weighted evidence combination method was proposed based on power-Pignistic probability distance.The conflict degree between two pieces of evidence was quantified by the power-Pignistic probability distance.After that,a similarity measure matrix was constructed,based on which the credibility of evidence was obtained.Then the weighted average method was used to revise the evidence.Finally,the fusion was accomplished by using Dempster’s rule.The results of the numerical examples show the efficiency and rationality of the proposed method.

Key words: Dempster-Shafer evidence theory, power-set-distribution Pignistic probability function, power-Pignistic probability distance, similarity/dissimilarity measure

CLC Number:

TP391

Jingwei ZHU,Xiaodan WANG,Yafei SONG,Wenlong HUANG. Weighted evidence combination method based on power-Pignistic probability distance[J]. Journal on Communications, 2018, 39(1): 117-125.

Figures/Tables 6

事件	m₂(θ₁)	m₂(θ₂)	m₂(θ₃)	m₂(θ₁,θ₂)	m₂(θ₁,θ₃)	m₂(θ₂,θ₃)	m₂(θ₁,θ₂,θ₃)
1	$\frac{1}{7}$	$\frac{1}{7}$	$\frac{1}{7}$	$\frac{1}{7}$	$\frac{1}{7}$	$\frac{1}{7}$	$\frac{1}{7}$
2	$\frac{1}{7} - \frac{Δ}{6}$	$\frac{1}{7} - \frac{Δ}{6}$	$\frac{1}{7} - \frac{Δ}{6}$	$\frac{1}{7} - \frac{Δ}{6}$	$\frac{1}{7} - \frac{Δ}{6}$	$\frac{1}{7} - \frac{Δ}{6}$	$\frac{1}{7} + Δ$
3	$\frac{1}{7} - \frac{2 Δ}{6}$	$\frac{1}{7} - \frac{2 Δ}{6}$	$\frac{1}{7} - \frac{2 Δ}{6}$	$\frac{1}{7} - \frac{2 Δ}{6}$	$\frac{1}{7} - \frac{2 Δ}{6}$	$\frac{1}{7} - \frac{2 Δ}{6}$	$\frac{1}{7} + 2 Δ$
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
19	$\frac{1}{7} - \frac{18 Δ}{6}$	$\frac{1}{7} - \frac{18 Δ}{6}$	$\frac{1}{7} - \frac{18 Δ}{6}$	$\frac{1}{7} - \frac{18 Δ}{6}$	$\frac{1}{7} - \frac{18 Δ}{6}$	$\frac{1}{7} - \frac{18 Δ}{6}$	$\frac{1}{7} + 18 Δ$
20	0	0	0	0	0	0	1

方法	$m_{1 \oplus 2} (A)$	$m_{1 \oplus 2} (B)$	$m_{1 \oplus 2} (C)$	$m_{1 \oplus 2} (Ω)$
Dempster规则	0	1	0	0
Yager法	0	0.000 1	0	0.999 9
改进Yager法	0.182	0.004	0.182	0.632
本文方法	0.499 9	0.000 2	0.499 9	0

方法	$m_{1 \oplus 2} (A)$	$m_{1 \oplus 2} (B)$	$m_{1 \oplus 2} (C)$	$m_{1 \oplus 2} (Ω)$
Dempster规则	0.949 2	0.033 9	0.016 9	0
Yager法	0.560 0	0.020 0	0.010 0	0.410 0
改进Yager法	0.764 1	0.060 8	0.037 2	0.137 9
本文方法	0.945 4	0.037 8	0.016 8	0

References 24

[1]	DEMPSTER A P . Upper and lower probabilities induced by a multi-valued mapping[J]. Annals of Mathematical Statistics, 1967,38(4): 325-339.
[2]	ZADEH L . A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination[J]. AI Magazine, 1986,7(2): 85-90.
[3]	YAGER R R . On the Dempster-Shafer framework and new combination rules[J]. Information Sciences, 1987,41(2): 93-137.
[4]	SMETS P . The combination of evidence in the transferable belief model[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990,12(5): 447-458.
[5]	孙全, 叶秀清, 顾伟康 . 一种新的基于证据理论的合成公式[J]. 电子学报, 2000,28(8): 117-119.
	SUN Q , YE X Q , GU W K . A new combination rule of evidence[J]. Acta Electronica Sinica, 2000,28(8): 117-119.
[6]	LEFEVRE E , COLOT O , VANNOORENBERGHE P . Belief functions combination and conflict management[J]. Information Fusion, 2002,3(2): 149-162.
[7]	FU Y W , YANG W . Combination rule based on proportional redistribution of generalized conflict for evidence theory[J]. Chinese Journal of Electronics, 2014,23(3): 533-538.
[8]	权文, 王晓丹, 王坚 ,等. 一种基于局部冲突分配的 DST 组合规则[J]. 电子学报, 2012,40(9): 1880-1884.
	QUAN W , WANG X D , WANG J ,et al. New combination rule of DST based on local conflict distribution strategy[J]. Acta Electronica Sinica, 2012,40(9): 1880-1884.
[9]	陈圣群, 王应明 . 证据的分组合成法[J]. 控制与决策, 2013,28(4): 574-578.
	CHEN S Q , WANG Y M . Grouping method for combining evidence[J]. Control and Decision, 2013,28(4): 574-578.
[10]	张鑫, 牟龙华 . 基于局部冲突消除的证据合成法则[J]. 系统工程与电子技术, 2016,38(7): 1594-1599.
	ZHANG X , MU L H . Evidence combination rule based on local con-flict elimination[J]. Systems Engineering and Electronics, 2016,38(7): 1594-1599.
[11]	陈雁飞, 夏学知, 胡丹桂 ,等. 基于试探折扣修正的证据组合方法[J]. 电子学报, 2014,42(4): 756-765.
	CHEN Y F , XA X Z , HU D G ,et al. Evidence combination based on tentative discount of evidences[J]. Acta Electronica Sinica, 2014,42(4): 756-765.
[12]	罗贺, 尹艳平, 胡笑旋 ,等. 基于可信因子的证据源修正方法[J]. 系统工程与电子技术, 2015,37(6): 1459-1464.
	LUO H , YIN Y P , HU X X ,et al. Method to modify evidence source based on trustworthy factors[J]. Systems Engineering and Electronics, 2015,37(6): 1459-1464.
[13]	WEN C L , WANG Y C , XU X B . Fuzzy information fusion algorithm of fault diagnosis based on similarity measure of evidence[C]// Advances in Neural Networks Lecture Notes in Computer Science. 2008: 506-515.
[14]	YU C , YANG J H , YANG D B ,et al. An improved conflicting evidence combination approach based on a new supporting probability distance[J]. Expert Systems with Applications, 2015,42(12): 5139-5149.
[15]	毕文豪, 张安, 李冲 . 基于新的证据冲突衡量的加权证据融合方法[J]. 控制与决策, 2016,31(1): 73-78.
	BI W H , ZHANG A , LI C . Weighted evidence combination method based on new evidence conflict measurement approach[J]. Control and Decision, 2016,31(1): 73-78.
[16]	MURPHY C K . Combining belief functions when evidence conflicts[J]. Decision Support Systems, 2000,29(1): 1-9.
[17]	邓勇, 施文康, 朱振福 . 一种有效处理冲突证据的组合方法[J]. 红外与毫米波学报, 2004,23(1): 27-32.
	DENG Y , SHI W K , ZHU Z F . Efficient combination approach of con-flict evidence[J]. J Infrared Millim Waves, 2004,23(1): 27-32.
[18]	肖建于, 童敏明, 朱昌杰 ,等. 基于 Pignistic 概率距离的改进证据组合规则[J]. 上海交通大学学报, 2012,46(4): 636-645.
	XIAO J Y , TONG M M , ZHU C J ,et al. Improved combination rule of evidence based on Pignistic probability distance[J]. Journal of Shang-hai Jiaotong University, 2012,46(4): 636-645.
[19]	JOUSSELME A L , MAUPIN P . Distances in evidence theory:comprehensive survey and generalizations[J]. International Journal of Approximate Reasoning, 2012,53(2): 118-145.
[20]	JOUSSELME A L , GRENIER D , BOSSE E . A new distance between two bodies of evidence[J]. Information Fusion, 2001,2(1): 91-101.
[21]	TESSEM B . Approximations for efficient computation in the theory of evidence[J]. Artificial Intelligence, 1993,61(2): 315-329.
[22]	李昌玺, 周焰, 王盛超 ,等. 多源信息融合中一种新的证据合成算法[J]. 上海交通大学学报, 2016,50(7): 1125-1131.
	LI C X , ZHOU Y , WANG S C ,et al. A novel combination rule of evi-dence theory in multi-source information fusion[J]. Journal of Shang-hai Jiaotong University, 2016,50(7): 1125-1131.
[23]	王亮, 吕卫民, 滕克难 ,等. 基于分类修正的多证据合成方法[J]. 控制与决策, 2015,30(1): 125-130.
	WANG L , LV W M , TENG K N ,et al. Combination method of mul-ti-evidence based on classification correction[J]. Control and Decision, 2015,30(1): 125-130.
[24]	HAN D Q , DENG Y , HAN C Z ,et al. Some notes on betting commitment distance in evidence theory[J]. Science China-Information Sciences, 2012,55(3): 558-565.

Metrics

Recommended 0

No Suggested Reading articles found!

事件	1?d_Bet	sim_Ta	1?d_SP	1?d_J	cosθ	1?d_PBet
1	0.333 3	0.333 3	0.428 6	0.382 8	0.378 0	0.258 5
2	0.333 3	0.333 3	0.406 0	0.376 4	0.355 1	0.252 4
3	0.333 3	0.333 3	0.383 5	0.369 5	0.327 5	0.246 3
4	0.333 3	0.333 3	0.360 9	0.362 0	0.296 9	0.240 2
5	0.333 3	0.333 3	0.338 3	0.354 0	0.265 2	0.234 2
6	0.333 3	0.333 3	0.315 8	0.345 4	0.234 1	0.228 1
7	0.333 3	0.333 3	0.293 2	0.336 4	0.204 6	0.222 0
8	0.333 3	0.333 3	0.270 7	0.327 0	0.177 2	0.215 9
9	0.333 3	0.333 3	0.248 1	0.317 0	0.152 3	0.209 8
10	0.333 3	0.333 3	0.225 6	0.306 7	0.129 9	0.203 7
11	0.333 3	0.333 3	0.203 0	0.295 9	0.109 7	0.197 6
12	0.333 3	0.333 3	0.180 5	0.284 8	0.091 7	0.191 6
13	0.333 3	0.333 3	0.157 9	0.273 3	0.075 6	0.185 5
14	0.333 3	0.333 3	0.135 3	0.261 4	0.061 2	0.179 4
15	0.333 3	0.333 3	0.112 8	0.249 1	0.048 2	0.173 3
16	0.333 3	0.333 3	0.090 2	0.236 6	0.036 5	0.167 2
17	0.333 3	0.333 3	0.067 7	0.223 8	0.026 0	0.161 1
18	0.333 3	0.333 3	0.045 1	0.210 6	0.016 5	0.155 0
19	0.333 3	0.333 3	0.022 6	0.197 2	0.007 9	0.148 9
20	0.333 3	0.333 3	0.333 3	0.183 5	0	0.142 9

方法	m₁ ,m2	m₁ ,m₂ ,m₃	m ₁,m₂,m₃,m₄	m ₁,m₂,m₃,m₄,m₅
	m (A)=0	m (A)=0	m (A)=0	m (A)=0
Dempster规则	m(B)=0.857 1	m(B)=0.631 6	m(B)=0.328 8	m(B)=0.140 4
	m(C)=0.142 9	m(C)=0.368 4	m(C)=0.671 2	m(C)=0.859 6
	m (A)=0	m (A)=0	m (A)=0	m (A)=0
Yager法	m(B)=0.18	m(B)=0.018	m(B)=0.001 8	m(B)=0.000 18
	m(C)=0.03	m(C)=0.010 5	m(C)=0.003 68	m(C)=0.00110
	m(ABC)=0.79	m(ABC)=0.971 5	m(ABC)=0.994 52	m(ABC)=0.998 72
	m (A)=0	m(A)=0.637 3	m(A)=0.902 6	m(A)=0.963 1
Wen法(cosθ法)	m(B)=0.857 1	m(B)=0.143 6	m(B)=0.007 3	m(B)=0.001 1
	m(C)=0.142 9	m(C)=0.219 1	m(C)=0.083 2	m(C)=0.026 0
			m(AC)=0.007 0	m(AC)=0.009 8
	m (A)=0	m(A)=0.636 4	m(A)=0.892 4	m(A)=0.960 5
Yu法(d_SP法)	m(B)=0.857 1	m(B)=0.142 4	m(B)=0.008 2	m(B)=0.001 1
	m(C)=0.142 9	m(C)=0.2211	m(C)=0.070 0	m(C)=0.020 6
			m(AC)=0.029 3	m(AC)=0.017 8
	m (A)=0	m(A)=0.706 3	m(A)=0.908 4	m(A)=0.965 9
sim_Ta法	m(B)=0.857 1	m(B)=0.087 0	m(B)=0.005 7	m(B)=0.000 8
	m(C)=0.142 9	m(C)=0.206 7	m(C)=0.083 0	m(C)=0.027 0
			m(AC)=0.003 0	m(AC)=0.006 3
	m(A)=0.154 3	m(A)=0.556 8	m(A)=0.865 3	m(A)=0.968 8
Murphy法	m(B)=0.746 9	m(B)=0.356 2	m(B)=0.089 1	m(B)=0.015 6
	m(C)=0.098 8	m(C)=0.078 1	m(C)=0.038 2	m(C)=0.012 7
		m(AC)=0.008 8	m(AC)=0.007 5	m(AC)=0.002 9
	m(A)=0.154 3	m(A)=0.736 9	m(A)=0.948 4	m(A)=0.986 9
d _J 法	m(B)=0.746 9	m(B)=0.161 8	m(B)=0.012 0	m(B)=0.001 0
	m(C)=0.098 8	m(C)=0.091 5	m(C)=0.031 0	m(C)=0.008 8
		m(AC)=0.009 8	m(AC)=0.008 6	m(AC)=0.003 2
	m(A)=0.154 3	m(A)=0.764 0	m(A)=0.952 0	m(A)=0.987 4
本文(d_PBet法)	m(B)=0.746 9	m(B)=0.135 1	m(B)=0.009 5	m(B)=0.000 8
	m(C)=0.098 8	m(C)=0.090 1	m(C)=0.029 6	m(C)=0.008 5
		m(AC)=0.010 8	m(AC)=0.009 0	m(AC)=0.003 3

Weighted evidence combination method based on power-Pignistic probability distance

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 6

References 24

Related Articles 6

Metrics

Recommended 0

[1]	Zhiguo SUN, Xinyue REN, Zengmao CHEN, Ming DIAO. Cooperative spectrum sensing method and performance analysis based on similarity between evidences [J]. Journal on Communications, 2020, 41(12): 139-147.
[2]	Lu WANG,Qing-hua XING,Yi-fan MAO. Directional evidence conflict measurement approach [J]. Journal on Communications, 2016, 37(7): 118-123.
[3]	. Measurement of evidence conflict based on correlation coefficient [J]. Journal on Communications, 2014, 35(5): 13-100.
[4]	Ya-fei SONG,Xiao-dan WANG,Lei LEI,Ai-jun XUE. Measurement of evidence conflict based on correlation coefficient [J]. Journal on Communications, 2014, 35(5): 95-100.
[5]	Ya-jian ZHOU,Kai LIU,Lin XIAO. Weighted cooperative spectrum sensing algorithm based on dempster-shafer evidence theory [J]. Journal on Communications, 2012, 33(12): 19-24.
[6]	Kai YANG,Jian-feng MA,Chao YANG. Trusted routing based on D-S evidence theory in wireless mesh network [J]. Journal on Communications, 2011, 32(5): 89-96.