基于本征向量和Jousselme距离的高冲突证据融合方法

doi:10.12305/j.issn.1001-506X.2022.07.13

摘要/Abstract

摘要：

针对传统Dempster-Shafer (D-S)理论无法有效融合高冲突证据的问题, 提出了基于本征向量和Jousselme距离的证据修改方法。首先, 由决策者结合主观经验根据原始证据的重要性给出判断矩阵, 并利用本征向量法解得主观权重。接着, 由原始证据间的Jousselme距离得到客观权重, 然后, 综合主客观权重对原始证据进行修改。最后, 对修改后的证据体使用D-S理论进行融合。仿真结果表明, 该方法在对高冲突证据进行融合时收敛速度快, 准确度高, 同时具备良好的适应能力, 很好地解决了高冲突证据的融合问题。

关键词: 多传感器融合, Dempster-Shafer证据理论, 本征向量法, Jousselme距离

Abstract:

Aiming at the problem that the traditional Dempster-Shafer (D-S) theory cannot effectively integrate highly conflict evidence, an evidence modification method based on eigenvector and Jousselme distance is proposed. First, the decision maker combines subjective experience to give a judgment matrix based on the relative importance of the original evidence and uses the eigenvector method to solve the subjective weight. Then calculate the Jousselme distance between the original evidence to obtain the objective weight and combine the subjective and objective weights to modify the original evidence. Finally, the D-S theory is used to fuse the revised evidence body. The simulation results show that the method has fast convergence speed and high accuracy when fusing highly conflict evidence, and at the same time has good adaptability, and it solves the fusion problem of heavy conflict evidence.

Key words: multi-sensor fusion, Dempster-Shafer (D-S) evidence theory, eigenvector method, Jousselme distance

中图分类号:

TP391

刘康, 何明浩, 韩俊, 王庚. 基于本征向量和Jousselme距离的高冲突证据融合方法[J]. 系统工程与电子技术, 2022, 44(7): 2175-2180.

Kang LIU, Minghao HE, Jun HAN, Geng WANG. A high conflict evidence fusion method based on eigenvector and Jousselme distance[J]. Systems Engineering and Electronics, 2022, 44(7): 2175-2180.

图/表 11

表1

表2

图1

表3

表4

表5

图2

图3

图4

图5

图6

参考文献 21

1	MI X J , LV T X , TIAN Y , et al. Multi-sensor data fusion based on soft likelihood functions and OWA aggregation and its application in target recognition system[J]. ISA Transactions, 2021, 112, 137- 149. doi: 10.1016/j.isatra.2020.12.009
2	GONG Y M , MA Z Y , WANG M J , et al. A new multi-sensor fusion target recognition method based on complementarity ana-lysis and neutrosophic set[J]. Symmetry, 2020, 12 (9): 1435. doi: 10.3390/sym12091435
3	赵照, 吴晓锋. 基于多地并行融合的多传感器目标识别信息融合方法[J]. 指挥控制与仿真, 2020, 42 (2): 23- 27. doi: 10.3969/j.issn.1673-3819.2020.02.005
	ZHAO Z , WU X F . Multi-sensor target recognition information fusion method based on multi-location parallel fusion[J]. Command Control and Simulation, 2020, 42 (2): 23- 27. doi: 10.3969/j.issn.1673-3819.2020.02.005
4	LI J , YANG X Z , ZHOU L . Multi-sensor target recognition based-on multi-period improved DS evidence fusion method[J]. Journal of Nanoelectronics and Optoelectronics, 2018, 13 (5): 758- 767. doi: 10.1166/jno.2018.2325
5	ZENG H , YANG B , WANG X Q , et al. RGB-D object recognition using multi-modal deep neural network and DS evidence theory[J]. Sensors, 2019, 19 (3): 539. doi: 10.3390/s19030539
6	DUBOIS D , PRADE H . Representation and combination of uncertainty with belief functions and possibility measures[J]. Computational Intelligence, 2010, 4 (3): 244- 264.
7	LEFEVRE E , COLOT O , VANNOORENBERGHE P . Belief function combination and conflict management[J]. Information Fusion, 2002, 3 (2): 149- 162. doi: 10.1016/S1566-2535(02)00053-2
8	YAGER R R . On the aggregation of prioritized belief structure[J]. IEEE Trans.on System, Man, and Cybernetics-Part A: Systems and Humans, 1996, 26 (6): 708- 719. doi: 10.1109/3468.541331
9	YAGER R R . On the Dempster-Shafer framework and new combination rules[J]. Information Sciences, 1987, 41 (2): 93- 137. doi: 10.1016/0020-0255(87)90007-7
10	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. doi: 10.3321/j.issn:0372-2112.2000.08.036
	SUN Q , YE X Q , GU W K . A new synthetic formula based on evidence theory[J]. Acta Electronica Sinica, 2000, 28 (8): 117- 119. doi: 10.3321/j.issn:0372-2112.2000.08.036
11	HAENNI R , LEHMANN N . Resource bounded and anytime approximation of belief function computations[J]. International Journal of Approximate Reasoning, 2002, 31 (1): 103- 154.
12	LIU W R . Analyzing the degree of conflict among belief functions[J]. Artificial Intelligence, 2006, 170 (11): 909- 924. doi: 10.1016/j.artint.2006.05.002
13	MURPHY C . Combining belief functions when evidence conflicts[J]. Decision Support Systems, 2000, 29 (1): 1- 9. doi: 10.1016/S0167-9236(99)00084-6
14	DENG Y , SHI W K . Combining belief functions based on distance of evidence[J]. Decision Support Systems, 2004, 38 (3): 489- 493. doi: 10.1016/j.dss.2004.04.015
15	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. doi: 10.3321/j.issn:1001-9014.2004.01.006
	DENG Y , SHI W K , ZHU Z F . A combined method to effectively deal with conflicting evidence[J]. Journal of Infrared and Millimeter Waves, 2004, 23 (1): 27- 32. doi: 10.3321/j.issn:1001-9014.2004.01.006
16	岳超源. 决策理论与方法[M]. 北京: 科学出版社, 2019.
	YUE C Y . Decision theory and method[M]. Beijing: Science Press, 2019.
17	JUAN G , GAN J , WANG C X . The investment model of aviation industry VCGF based on AHP analysis of computer simulation[J]. Journal of Physics: Conference Series, 2020, 1578 (1): 012081. doi: 10.1088/1742-6596/1578/1/012081
18	张欢, 陆见光, 唐向红. 面向冲突证据的改进DS证据理论算法[J]. 北京航空航天大学学报, 2020, 46 (3): 616- 623.
	ZHANG H , LU J G , TANG X H . Improved DS evidence theory algorithm for conflict evidence[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46 (3): 616- 623.
19	尹东亮, 黄晓颖, 吴艳杰. 基于云模型和改进D-S证据理论的目标识别决策方法研究[J]. 航空学报, 2021, 42 (7): 247- 268.
	YIN D L , HUANG X Y , WU Y J . Research on target recognition decision-making method based on cloud model and improved D-S evidence theory[J]. Journal of Aeronautics, 2021, 42 (7): 247- 268.
20	ZHAO J , XUE R , DONG Z N , et al. Evaluating the reliability of sources of evidence with a two-perspective approach in classification problems based on evidence theory[J]. Information Sciences, 2020, 507, 313- 338. doi: 10.1016/j.ins.2019.08.033
21	FLORENTIN S , NASSIM A , YOUCEF C , et al. PCR5 and neutrosophic probability in target identification (revisited)[J]. Neutrosophic Sets and Systems, 2017, 16, 76- 79.

相对重要程度	定义
1	同等重要
3	略微重要
5	相当重要
7	明显重要
9	绝对重要
2, 4, 6, 8	两个相邻判断的中间值

n	2	3	4	5	6	7
RI	0.00	0.58	0.90	1.12	1.24	1.32

证据	m₁	m₂	m₃	m₄	m₅
m₁	1	3	1	1	1
m₂	1/3	1	1/3	1/3	1/4
m₃	1	3	1	1	1
m₄	1	3	1	1	1
m₅	1	4	1	1	1

证据	m₁	m₂	m₃	m₄	m₅
m₁	0	0.430 1	0.158 1	0.079 1	0.079 1
m₂	0.430 1	0	0.360 6	0.388 9	0.459 6
m₃	0.158 1	0.360 6	0	0.079 1	0.127 5
m₄	0.079 1	0.388 9	0.079 1	0	0.070 7
m₅	0.079 1	0.459 6	0.127 5	0.070 7	0

算法名称	m₁, m₂	m₁, m₂, m₃	m₁, m₂, m₃, m₄	m₁, m₂, m₃, m₄, m₅
D-S证据理论	m(A)=0.000 0	m(A)=0.000 0	m(A)=0.000 0	m(A)=0.000 0
	m(B)=0.727 3	m(B)=0.888 9	m(B)=0.909 1	m(B)=0.882 4
	m(C)=0.272 7	m(C)=0.111 1	m(C)=0.090 9	m(C)=0.117 6
Yager组合规则	m(A)=0.000 0	m(A)=0.000 0	m(A)=0.000 0	m(A)=0.000 0
	m(B)=0.160 0	m(B)=0.048 0	m(B)=0.012 0	m(B)=0.001 8
	m(C)=0.060 0	m(C)=0.006 0	m(C)=0.001 2	m(C)=0.000 2
	m(X)=0.780 0	m(X)=0.946 0	m(X)=0.986 8	m(X)=0.998 0
孙全组合规则	m(A)=0.089 4	m(A)=0.170 5	m(A)=0.206 2	m(A)=0.236 9
	m(B)=0.338 8	m(B)=0.249 5	m(B)=0.205 7	m(B)=0.176 9
	m(C)=0.149 4	m(C)=0.099 0	m(C)=0.101 2	m(C)=0.103 2
	m(X)=0.422 4	m(X)=0.481 0	m(X)=0.486 9	m(X)=0.483 0
murphy组合规则	m(A)=0.166 7	m(A)=0.355 5	m(A)=0.545 3	m(A)=0.809 0
	m(B)=0.666 7	m(B)=0.586 8	m(B)=0.424 6	m(B)=0.178 5
	m(C)=0.166 6	m(C)=0.057 7	m(C)=0.030 1	m(C)=0.012 5
邓勇组合规则	m(A)=0.166 7	m(A)=0.497 8	m(A)=0.741 8	m(A)=0.927 7
	m(B)=0.666 7	m(B)=0.443 4	m(B)=0.231 2	m(B)=0.063 3
	m(C)=0.166 6	m(C)=0.058 8	m(C)=0.027 0	m(C)=0.009 0
PCR5规则	m(A)=0.225 3	m(A)=0.440 8	m(A)=0.551 5	m(A)=0.703 7
	m(B)=0.600 7	m(B)=0.483 7	m(B)=0.368 2	m(B)=0.215 0
	m(C)=0.174 0	m(C)=0.075 5	m(C)=0.080 3	m(C)=0.081 3
本文规则	m(A)=0.394 2	m(A)=0.644 8	m(A)=0.802 3	m(A)=0.942 2
	m(B)=0.294 9	m(B)=0.256 6	m(B)=0.150 9	m(B)=0.040 9
	m(C)=0.285 6	m(C)=0.096 8	m(C)=0.046 8	m(C)=0.016 9
	m(X)=0.025 4	m(X)=0.001 8	m(X)=0.000 1