基于改进策略的DS证据融合算法

doi:10.12305/j.issn.1001-506X.2026.02.23

摘要/Abstract

摘要：

针对数据融合与决策过程中存在的不确定性问题，尤其是冲突悖论问题，提出基于改进策略的Dempster-Shafer (DS)证据融合算法。算法通过对证据体在约束条件下进行“调增”和“调减”修改，实现证据支持度重新分配，进而支持利用DS证据理论合成公式获得更加可靠、合理、稳定、准确的数据融合结果，同时引入Jensen-Shannon散度概念对算法参数与散度计算结果之间的关系进行量化分析。采用包含全冲突悖论、0信任悖论、1信任悖论、高冲突悖论等在内的8个冲突悖论案例对算法进行仿真分析，明确算法参数取值范围，并与现有多种改进算法进行结果比较。结果表明，当算法调增量取值介于最小概率值的0.775~0.999倍时，算法在最大限度保留原始数据分布特点的基础上能够获得符合人类正常认知的结果。最后，将该算法进一步应用于目标意图推理，该算法能够得到准确的数据融合和推理结果。

关键词: 数据决策, 冲突悖论, 证据理论, 改进策略, Jensen-Shannon散度

Abstract:

Aiming at the uncertainty issues present in data fusion and decision-making processes, particularly the conflict paradox problems, an improved strategy-based Dempster-Shafer （DS） evidence fusion algorithm is proposed. The algorithm achieves the reallocation of evidence support by adjusting the evidence bodies through “increasing” and “decreasing” modifications under constraints. This supports the use of the DS evidence theory synthesis formula to obtain more reliable, reasonable, stable, and accurate data fusion results. Additionally, the concept of Jensen-Shannon divergence is introduced to quantitatively analyze the relationship between algorithm parameters and divergence calculation results. The algorithm is simulated and analyzed using eight conflict paradox cases, including complete conflict paradox, zero trust paradox, one trust paradox, and high conflict paradox, to define the range of algorithm parameters and compare the results with various existing improved algorithms. The results show that when the algorithm’s adjustment increment is between 0.775 to 0.999 times the minimum probability value, the algorithm can achieve results that align with normal human cognition while maximally preserving the characteristics of the original data distribution. The algorithm is further applied to target intention reasoning, where it is able to obtain accurate data fusion and reasoning results.

Key words: data decision-making, conflict paradox, evidence theory, improved strategies, Jensen-Shannon divergence

中图分类号:

TP 182

刘科, 曾行, 李鑫龙. 基于改进策略的DS证据融合算法[J]. 系统工程与电子技术, 2026, 48(2): 627-637.

Ke LIU, Xing ZENG, Xinlong LI. DS evidence fusion algorithm based on improved strategy[J]. Systems Engineering and Electronics, 2026, 48(2): 627-637.

图/表 24

图1

图2

图3

图4

图5

图6

图7

图8

表1

表2

表3

表4

表5

表6

表7

表8

图9

图10

图11

图12

图13

图14

图15

图16

参考文献 50

1	ZHOU C, XU D, CAO Z D. Multi-source data fusion method of equipment maintainability based on improved DS evidence theory[C]// Proc. of the 5th International Conference on System Reliability and Safety Engineering, 2023.
2	刘庆利, 王文广, 张学翠, 等. 基于改进DS证据理论的指挥控制系统信息融合方法[J]. 火力与指挥控制, 2022, 47 (2): 82- 87. doi: 10.3969/j.issn.1002-0640.2022.02.014
	LIU Q L, WANG W G, ZHANG X C, et al. Information fusion method of command and control system based on improved DS evidence theory[J]. Fire Control & Command Control, 2022, 47 (2): 82- 87. doi: 10.3969/j.issn.1002-0640.2022.02.014
3	SAHU A, DAVIS K. Inter-domain fusion for enhanced intrusion detection in power systems: an evidence theoretic and meta-heuristic approach[J]. Sensors, 2022, 22 (6): 2100. doi: 10.3390/s22062100
4	SANCHEZ L, VASILE M, SANVIDO S, et al. Treatment of epistemic uncertainty in conjunction analysis with Dempster-Shafer theory[J]. Advances in Space Research, 2024, 74 (11): 5639- 5686. doi: 10.1016/j.asr.2024.09.014
5	LIU J H, ZHANG P, SUN J, et al. Automatic recognition method of relative position and pose between rescue robot and stairs[C]// Proc. of the 18th Chinese Intelligent Systems Conference, 2022.
6	LIU P G, HE P, GAO X B, et al. Research on multi-sensor fusion algorithm based on improved DS evidence theory[C]// Proc. of the 15th International Conference on Communication Software and Networks, 2023.
7	徐浩, 邢清华, 王伟. 基于DST-IFS的空中目标敌我属性综合识别[J]. 系统工程与电子技术, 2017, 39 (8): 1757- 1764. doi: 10.3969/j.issn.1001-506X.2017.08.14
	XU H, XING Q H, WANG W. Integrated air target identification of friend or foe based on DST-IFS[J]. Systems Engineering and Electronics, 2017, 39 (8): 1757- 1764. doi: 10.3969/j.issn.1001-506X.2017.08.14
8	KHAN N, ANWAR S. Improved Dempster-Shafer sensor fusion using distance function and evidence weighted penalty: application in object detection[C]// Proc. of the 16th International Conference on Informatics in Control, Automation and Robotics, 2019.
9	GUO G H, LIU X B. The application and improvement of Dempster-Shafer evidence theory in communication signal recognition[C]// Proc. of the 5th Global Symposium on Millimeter-Waves, 2012.
10	LIU N K, ZHOU Z F, ZHU L J, et al. Fault diagnosis of unmanned aerial systems using the Dempster-Shafer evidence theory[J]. Actuators, 2024, 13 (7): 264. doi: 10.3390/act13070264
11	LIU H B, MA Z Y, DENG X Y, et al. A new method to air target threat evaluation based on Dempster-Shafer evidence theory[C]// Proc. of the 30th Chinese Control and Decision Conference, 2018.
12	BAI L, DU C L, CHEN J C. An information fusion positioning algorithm based on extended Dempster-Shafer evidence theory[C]// Proc. of the International Conference on Sensing, Diagnostics, Prognostics, and Control, 2019.
13	CHEN Y T, WANG Y, ZHAO Y B. A room-level indoor localization using an energy-harvesting BLE tag[J]. Electronics, 2024, 13 (22): 4493. doi: 10.3390/electronics13224493
14	WANG Y, LIU D S, YANG Y, et al. Target identity fusion method based on improved DS evidence theory[C]// Proc. of the 3rd International Conference on Electronic Information Engineering and Computer, 2023.
15	PETTURITI D, VANTAGGI B. Upper and lower conditional probabilities induced by a multivalued mapping[J]. Journal of Mathematical Analysis and Applications, 2018, 458 (2): 1214- 1235. doi: 10.1016/j.jmaa.2017.10.006
16	SHAFER G. A mathematical theory of evidence turns 40[J]. International Journal of Approximate Reasoning, 2016, 79 (SI): 7- 25.
17	ZHAO K Y, QIN P L, CAI S H, et al. A generalized weighted evidence fusion algorithm based on quantum modeling[J]. Information Sciences, 2024, 683, 121285. doi: 10.1016/j.ins.2024.121285
18	WANG Y B, XU X L, ZHAO Z Y, et al. Multisensors time-series change point detection in wireless sensor networks based on deep evidential fusion and self-distillation learning[J]. IEEE Internet of Things Journal, 2025, 12 (1): 1047- 1063.
19	李志强, 徐廷学, 顾钧元, 等. 融合不确定信息的某型导弹控制系统可靠性分析方法[J]. 系统工程与电子技术, 2017, 39 (12): 2869−2876.
	LI Z Q, XU T X, GU J Y, et al. Reliability analysis of a missile control system by fusing uncertain information[J]. Systems Engineering and Electronics, 2017, 39 (12): 2869−2876.
20	ZHANG X Z, LI J L, LI C, et al. Multi-teacher D-S fusion for semi-supervised SAR ship detection[J]. Remote Sensing, 2024, 16 (15): 2759. doi: 10.3390/rs16152759
21	YANG X, XIAO F Y. A novel uncertainty modeling method in complex evidence theory for decision making[J]. Engineering Applications of Artificial Intelligence, 2024, 133 (C): 108164.
22	HUANG Y C, XIAO F Y, CAO Z H, et al. Fractal belief renyi divergence with its applications in pattern classification[J]. IEEE Trans. on Knowledge and Data Engineering, 2024, 36 (12): 8297- 8312. doi: 10.1109/TKDE.2023.3342907
23	HUANG J J, XIAO F Y. Complex belief divergence measures for multisource information fusion[J]. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2025, 55 (2): 948- 962.
24	LIU Z. A new sine similarity measure based on evidence theory for conflict management [J]. Communications in Statistics-Theory and Methods, 2025, 54(11): 3350−3366.
25	DENG X Y, JIANG W. Upper bounds of uncertainty for Dempster combination rule-based evidence fusion systems[J]. IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2025, 55 (1): 817- 828.
26	张山鹰, 潘泉, 张洪才. 证据推理冲突问题研究[J]. 航空学报, 2001, 22 (4): 369- 372. doi: 10.3321/j.issn:1000-6893.2001.04.019
	ZHANG S Y, PAN Q, ZHANG H C. Conflict problem of Dempster-Shafer evidence theory[J]. Acta Aeronautica et Astronautica Sinica, 2001, 22 (4): 369- 372. doi: 10.3321/j.issn:1000-6893.2001.04.019
27	LIU Z G, PAN Q, DEZERT J. Classification of uncertain and imprecise data based on evidence theory[J]. Neurocomputing, 2014, 133, 459- 470. doi: 10.1016/j.neucom.2013.12.009
28	TIAN T, MING D L. Fusion of multi-measures in infrared target recognition based on Dempster-Shafer evidence theory[C]// Proc. of the 7th International Symposium on Multispectral Image Processing and Pattern Recognition, 2011.
29	张兵, 卢焕章. 多传感器自动目标识别中的冲突证据组合方法[J]. 系统工程与电子技术, 2006, 28 (6): 857- 860. doi: 10.3321/j.issn:1001-506X.2006.06.020
	ZHANG B, LU H Z. Combination method of conflict evidence in multi-sensor automatic target recognition[J]. Systems Engineering and Electronics, 2006, 28 (6): 857- 860. doi: 10.3321/j.issn:1001-506X.2006.06.020
30	郭华伟, 施文康, 刘清坤, 等. 一种新的证据组合规则[J]. 上海交通大学学报, 2006, 40 (11): 1895- 1900. doi: 10.3321/j.issn:1006-2467.2006.11.018
	GUO H W, SHI W K, LIU Q K, et al. A new combination rule of evidence[J]. Journal of Shanghai Jiaotong University, 2006, 40 (11): 1895- 1900. doi: 10.3321/j.issn:1006-2467.2006.11.018
31	DEZERT J, WANG P, TCHAMOVA A. On the validity of Dempster-Shafer theory[C]// Proc. of the 15th International Conference on Information Fusion, 2012.
32	TCHAMOVA A, DEZERT J. On the behavior of Dempster’s rule of combination and the foundations of Dempster-Shafer theory[C]// Proc. of the 6th IEEE International Conference Intelligent Systems, 2012.
33	陈杰. 基于DS证据理论的决策融合算法研究[D]. 哈尔滨: 哈尔滨工程大学, 2016.
	CHEN J. Research of decision fusion algorithm based on DS evidence theory[D]. Harbin: Harbin Engineering University, 2016.
34	LIU P L, XIAO F Y. Earth mover’s divergence of belief function[J]. Computational and Applied Mathematics, 2022, 41 (6): 292. doi: 10.1007/s40314-022-02000-3
35	CHEN L Y, DENG Y, CHEONG K H. Permutation Jensen–Shannon divergence for random permutation set[J]. Engineering Applications of Artificial Intelligence, 2023, 119, 105701. doi: 10.1016/j.engappai.2022.105701
36	ZHANG F X, CHEN Z C, CAI R. A reinforced final belief divergence for mass functions and its application in target recognition[J]. Applied Intelligence, 2025, 55 (2): 135. doi: 10.1007/s10489-024-05955-4
37	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 combination rules of evidence theory[J]. Acta Electronica Sinica, 2000, 28 (8): 117- 119. doi: 10.3321/j.issn:0372-2112.2000.08.036
38	MURPHYC K. Combining belief functions when evidence conflicts[J]. Decision Support Systems, 2000, 29 (1): 1- 9. doi: 10.1016/S0167-9236(99)00084-6
39	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
40	韩峰, 杨万海, 袁晓光. 一种有效处理冲突证据的组合方法[J]. 电光与控制, 2010, 17 (4): 5- 8. doi: 10.3969/j.issn.1671-637X.2010.04.002
	HAN F, YANG W H, YUAN X G. An efficient approach for conflict evidence combination[J]. Electronics Optics & Control, 2010, 17 (4): 5- 8. doi: 10.3969/j.issn.1671-637X.2010.04.002
41	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. An improved DS evidence theory algorithm for conflict evidence[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46 (3): 616- 623.
42	HORIUCHI T. Decision rule for pattern classification by integrating interval feature values[J]. IEEE Trans. on Pattern Analysis and Machine Intelligence, 1998, 20 (4): 440- 448. doi: 10.1109/34.677286
43	李弼程, 王波, 魏俊, 等. 一种有效的证据理论合成公式[J]. 数据采集与处理, 2002, 17 (1): 33- 36. doi: 10.3969/j.issn.1004-9037.2002.01.008
	LI B C, WANG B, WEI J, et al. An efficient combination rule of evidence theory[J]. Journal of Data Acquisition & Processing, 2002, 17 (1): 33- 36. doi: 10.3969/j.issn.1004-9037.2002.01.008
44	康健. 基于多传感器信息融合关键技术的研究[D]. 哈尔滨: 哈尔滨工程大学, 2013.
	KANG J. The key technology research of multi-sensors information fusion[D]. Harbin: Harbin Engineering University, 2013.
45	陈博, 万寿红, 岳丽华. 改进的DS证据舰船融合检测研究[J]. 计算机工程与应用, 2010, 46 (28): 222- 224.
	CHEN B, WAN S H, YUE L H. Study on ship detection with improved Dempster-Shafer theory[J]. Computer Engineering and Applications, 2010, 46 (28): 222- 224.
46	YAO J F, WU C P, XIE X B, et al. A new method of information decision-making based on D-S evidence theory[C]// Proc. of the IEEE International Conference on Systems, Man and Cybernetics, 2010.
47	FLOREA M C, JOUSSELME A L, BOSSE E, et al. Robust combination rules for evidence theory[J]. Information Fusion, 2009, 10 (2): 183- 197. doi: 10.1016/j.inffus.2008.08.007
48	LEFEVRE E, COLOT O, VANNOOREN-BERGHE P, et al. A generic framework for resolving the conflict in the combination of belief structures[C]// Proc. of the 3rd International Conference on Information Fusion, 2000.
49	JOSANG A, DANIEL M, VANNOOREN-BERGHE P. Strategies for combining conflicting dogmatic beliefs[C]// Proc. of the 6th International Conference on Information Fusion, 2003.
50	陈黎, 李芳芳, 邹长虹. 基于动态贝叶斯网络和模板匹配的空中目标意图识别[J]. 现代防御技术, 2023, 51 (2): 62- 70. doi: 10.3969/j.issn.1009-086x.2023.02.008
	CHEN L, LI F F, ZOU C H. Intension recognition of air-defense target based on dynamic Bayesian network and template matching[J]. Modern Defense Technology, 2023, 51 (2): 62- 70. doi: 10.3969/j.issn.1009-086x.2023.02.008

文献序号	$ A $	$ B $	$ C $
文献[37]	0.091 7	0.042 3	0.007 1
文献[38]	0.820 4	0.174 8	0.004 7
文献[39]	0	0	0
文献[40]	0.816 6	0.116 4	0.067 0
文献[41]	0.999 9	0	0.000 1
本文算法	0.975 0	0.014 1	0.010 9

文献序号	$ A $	$ B $	$ C $
文献[37]	0.052 5	0.059 7	0.037 7
文献[38]	0.409 1	0.409 1	0.181 8
文献[39]	0	0.727 3	0.272 7
文献[40]	0.431 8	0.295 5	0.272 7
文献[41]	0.978 1	0.015 9	0.006 0
本文算法	0.439 3	0.438 9	0.121 8

文献序号	$ A $	$ B $	$ C $
文献[37]	0.038 8	0.017 9	0.084 6
文献[38]	0.167 6	0.034 6	0.797 8
文献[39]	0	1	0
文献[40]	0.138 8	0.131 8	0.729 4
文献[41]	0	0.000 1	0.999 9
本文算法	0.016 9	0.004 1	0.979 0

文献序号	$ A $	$ B $	$ C $	$ D $	$ E $
文献[37]	0.044 3	0.016 3	0.016 3	0.004 5	0.011 8
文献[38]	0.763 7	0.103 1	0.071 6	0.008 0	0.053 8
文献[39]	0	0.357 1	0.428 6	0	0.214 3
文献[40]	0.532 4	0.152 1	0.146 2	0.045 1	0.124 1
文献[41]	0.998 8	0.000 5	0.000 3	0	0.000 3
本文算法	0.989 7	0.003 4	0.004 5	0.000 4	0.002 0

文献序号	$ A $	$ B $	$ C $
DS证据合成理论	0	0	1
文献[37]	0.320 6	0.003 4	0.188 6
文献[39]	0	0	0.000 1
文献[42]	0.626 7	0.006 7	0.366 7
文献[43]	0.626 0	0.006 7	0.367 3
本文算法	0.870 1	0.000 7	0.129 2