基于信任度和虚假度的证据组合方法

doi:10.11959/j.issn.1000-436x.2015104

摘要/Abstract

摘要：

D-S证据理论在信息融合领域有着广泛的应用，但使用Dempster组合规则对高冲突证据进行合成时可能会得到反直观的结果，在应用中也存在“一票否决”的问题，为解决这些问题，提出一种改进的基于证据信任度和虚假度的证据加权组合方法。首先在证据相关系数的基础上定义了证据信任度，再结合证据虚假度的概念来确定各原始证据的权重，依此权重系数对各证据进行加权平均后利用Dempster组合规则对加权平均证据进行组合。数值算例表明，该组合方法可实现冲突证据的有效融合，与其他方法相比该方法具有更好的收敛性。

关键词: D-S证据理论, 证据组合, 证据冲突, 相关系数, 信任度, 虚假度

Abstract:

D-S evidence theory has been widely used in various fields of information fusion due to its efficiency in deal-ing with uncertain information.Unfortunately,combination of conflicting evidences by classical Dempster's rule may produce counter-intuitive results.To alleviate this problem,a new weighted average combination rule is proposed.Defi-nitions of correlation coefficient was first presented,followed by the introduction of falsity.Then the credibility of evi-dence is proposed.A new weighted coefficient is determined by credibility and falsity.To achieve convergence,the nor-malized weighted coefficient was suggested into the Dempster's combination rule to average the basic probability as-signment.Comparable numerical examples demonstrate that the proposed approach can combine conflicting evidences more effectively.Moreover,the proposed methodology can provide a faster identification of the observed object.

Key words: D-S evidence theory, evidence combination, evidence conflict, correlation coefficient, credibility, falsity

宋亚飞,王晓丹,雷蕾,薛爱军. 基于信任度和虚假度的证据组合方法[J]. 通信学报, 2015, 36(5): 98-103.

ONGYa-fei S,ANGXiao-dan W,EILei L,UEAi-jun X. Evidence combination based on the degree of credibility and falsity[J]. Journal on Communications, 2015, 36(5): 98-103.

图/表 3

表1

本文证据组合方法与其他几种证据组合方法的比较"

证据组合方法

\oplus_{i = 1}^{2} m_{i}

\oplus_{i = 1}^{3} m_{i}

\oplus_{i = 1}^{4} m_{i}

\oplus_{i = 1}^{5} m_{i}

Dempster方法

m (A)=0

m(B)=0.791

m(C)=0.209

m (A)=0

m(B)=0.557

m(C)=0.443

m (A)=0

m(B)=0.759

m(C)=0.241

m (A)=0

m(B)=0.47

m(C)=0.526

Yager方法^[9]

m (A)=0

m(B)=0.170

m(C)=0.045

m(Θ)=0.785

m (A)=0

m(B)=0.017

m(C)=0.014

m(Θ)=0.969

m (A)=0

m(B)=0.004

m(C)=0.002

m(Θ)=0.994

m (A)=0

m(B)=0.0004

m(C)=0.0005

m(Θ)=0.9991

孙全方法^[11]

m (A)=0.090

m(B)=0.358

m(C)=0.126

m(Θ)=0.426

m(A)=0.168

m(B)=0.193

m(C)=0.128

m(Θ)=0.511

m(A)=0.217

m(B)=0.178

m(C)=0.107

m(Θ)=0.498

m(A)=0.234

m(B)=0.153

m(C)=0.122

m(Θ)=0.491

Murphy方法^[14]

m(A)=0.161

m(B)=0.709

m(C)=0.130

m(A)=0.407

m(B)=0.464

m(C)=0.129

m(A)=0.683

m(B)=0.279

m(C)=0.038

m(A)=0.865

m(B)=0.102

m(C)=0.033

邓勇方法^[15]

m(A)=0.161

m(B)=0.709

m(C)=0.130

m(A)=0.617

m(B)=0.232

m(C)=0.151

m(A)=0.870

m(B)=0.095

m(C)=0.035

m(A)=0.952

m(B)=0.020

m(C)=0.028

本文方法

m(A)=0.161

m(B)=0.709

m(C)=0.130

m(A)=0.665

m(B)=0.181

m(C)=0.154

m(A)=0.905

m(B)=0.063

m(C)=0.032

m(A)=0.964

m(B)=0.011

m(C)=0.025

表1

表2

表3

本文方法和文献[15]方法的比较"

证据组合方法

\oplus_{i = 1}^{2} m_{i}

\oplus_{i = 1}^{3} m_{i}

\oplus_{i = 1}^{4} m_{i}

\oplus_{i = 1}^{5} m_{i}

\oplus_{i = 1}^{6} m_{i}

邓勇方法^[15]

m (A)=0.8052

m(B)=0.1185

m(C)=0.0189

m(AB)=0.0539

m(AC)=0

m(BC)=0

m(ABC)=0.003 6

m(A)=0.5899

m(B)=0.3910

m(C)=0.0048

m(AB)=0.0142

m(AC)=0

m(BC)=0

m(ABC)=0.0001

m(A)=0.7133

m(B)=0.2738

m(C)=0.0050

m(AB)=0.0079

m(AC)=0

m(BC)=0

m(ABC)=0

m(A)=0.8110

m(B)=0.1814

m(C)=0.0045

m(AB)=0.0029

m(AC)=0

m(BC)=0.0002

m(ABC)=0

m(A)=0.7899

m(B)=0.1996

m(C)=0.0057

m(AB)=0.0044

m(AC)=0.0002

m(BC)=0.0002

m(ABC)=0

本文方法

m(A)=0.8052

m(B)=0.1185

m(C)=0.0189

m(AB)=0.0539

m(AC)=0

m(BC)=0

m(ABC)=0.003 6

m(A)=0.6258

m(B)=0.3562

m(C)=0.0049

m(AB)=0.0129

m(AC)=0

m(BC)=0

m(ABC)=0.0001

m(A)=0.7340

m(B)=0.2537

m(C)=0.0050

m(AB)=0.0073

m(AC)=0

m(BC)=0

m(ABC)=0

m(A)=0.8261

m(B)=0.1669

m(C)=0.0041

m(AB)=0.0026

m(AC)=0

m(BC)=0.0002

m(ABC)=0

m(A)=0.8141

m(B)=0.1782

m(C)=0.0043

m(AB)=0.0031

m(AC)=0.0001

m(BC)=0.0001

m(ABC)=0

表3

参考文献 24

[1]	DEMPSTER A P . Upper and lower probabilities induced by a multi-valued mapping[J]. Annals Math.Stat., 1967,38: 325-339.
[2]	SHAFER G . A Mathematical Theory of Evidence[M]. Princeton,NJ: Princeton University Press, 1976.
[3]	苗锐，陈国初，李月等．基于随机集含糊证据的风力发电机故障诊断方法[J]．电力系统自动化， 2012,36(7):22-26. MIAO R , CHEN G C , LI Y , et al. A wind turbine fault diagnosis method based on vague evidence of random set[J]. Automation of Electric Power Systems, 2012,36(7):22-26.
[4]	雷蕾，王晓丹，邢雅琼等．结合 SVM 和 DS 证据理论的多极化HRRP分类研究[J]．控制与决策， 2013,28(6):861-866. LEI L , WANG X D , XING Y Q , et al. Multi-polarized HRRP classification by SVM and DS evidence theory[J]. Control and Decision, 2013,28(6):861-866.
[5]	刘帅奇，胡绍海，肖扬等．基于局部混合滤波的SAR图像边缘检测[J]．电子与信息学报， 2013,35(5):1120-1127. LIU S Q , HU S H , XIAO Y , et al. SAR image edge detection based on local hybrid filter[J]. Journal of Electronics ＆ Information Technology, 2013,35(5):1120-1127.
[6]	ZADEH L . Review of a mathematical theory of evidence[J]. AI Magazine, 1984,5(3): 81-83.
[7]	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.
[8]	郭华伟，施文康，邓勇等．证据冲突：丢弃，发现或化解？[J]．系统工程与电子技术， 2007,29(6):890-898. GUO H W , SHI W K , DENG Y , et al. Evidential conflict and its 3D strategy:discard,discover and disassemble?[J]. Systems Engineering and Electronics, 2007,29(6):890-898.
[9]	YAGER R.R . On the Dempster-Shafer framework and new combination rules[J]. Information Sciences, 1987,41(5): 93-138.
[10]	LEFEVRE E , COLOT O , VANNOORENBERGHE P . Belief function combination and conflict management[J]. Information Fusion, 2002,3(2): 149-162.
[11]	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 rules of evidence theory[J]. Acta Electronica Sinica, 2000,28(8):117-119.
	邓勇，施文康．一种改进的证据推理组合规则[J]．上海交通大学学报， 2003,37(8):1275-1278. DENG Y , SHI W K . A modified combination rule of evidence theory[J]. Journal of Shanghai Jiaotong University, 2003,37(8):1275-1278.
[13]	HAENNI R . Are alternative to Dempster's rule of combination real alternative? Comments on about the belief function combination and the conflict management problem-E lefevre[J]. Information,Fusion, 2002,3(3): 237-239.
[14]	MURPHY C K . Combining belief functions when evidence conflicts[J]. Decision support systems, 2000,29(1): 1-9.
[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. DENG Y , SHI W K , ZHU Z F . Efficient combination approach of conflict evidence[J]. J Infrared Millim Waves, 2004,23(1):27-32.
[16]	HAN D Q , DENG Y , HAN C Z . Weighted evidence combination based on distance of evidence and uncertainty measure[J]. J Infrared Millim Waves, 2011,30(5): 396-400.
[17]	FABRE S , APPRIOU A , BRIOTTET X . Presentation and description of two classification methods using data fusion based on sensor management[J]. Information Fusion, 2001,2(1): 49-71.
[18]	胡昌华，司小胜，周志杰等．新的证据冲突衡量标准下的 DS 改进算法[J]．电子学报， 2009,37(7):1578-1583. HU C H , SI X S , ZHOU Z J , et al. An improved D S algorithm under the new measure criteria of evidence conflict[J]. Acta Electronica Sinica, 2009,37(7):1578-1583.
[19]	许丽佳． D-S 理论在信息融合中的改进[J]．系统工程与电子技术， 2004,26(6):717-720. XU L J . Improvement of D S theory in an information fusion system[J]. Systems Engineering and Electronics, 2004,26(6):717-720.
[20]	周皙，徐晓滨，文成林等．冲突证据融合的优化方法[J]．自动化学报， 2012,38(6):976-985. ZHOU Z , XU X B , WEN C L , et al. An optimal method for combining conflicting evidences[J]. Acta Automatica Sinica, 2012,38(6):976-985.
[21]	JOUSSELME A L , GRENIER D , BOSSE E . A new distance between two bodies of evidence[J]. Information Fusion, 2001,(2): 91-101.
[22]	宋亚飞，王晓丹，雷蕾等．基于相关系数的证据冲突度量方法[J]．通信学报， 2014,35(5):95-100. SONG Y F , WANG X D , LEI L , et al. Measurement of evidence conflict based on correlation coefficient[J]. Journal on Communications, 2014,35(5):95-100.
[23]	SCHUBERT J . Conflict management in Dempster-Shafer theory using the degree of falsity[J]. International Journal of Approximate Reasoning, 2011,52(3): 449-460.
[24]	冯德军，王博，王伟．弹道中段雷达目标识别研究进展综述[J]．中国电子科学研究院学报， 2013,8(2):142-148. FENG D J , WANG B , WANG W . Overview of progress in midcourse radar target recognition[J]. Journal of CAEIT, 2013,8(2):142-148.

[1]	王欣, 付威. 基于推土机距离的证据冲突强度量方法[J]. 通信学报, 2022, 43(5): 204-213.
[2]	郭兴林, 孙振晓, 周昱瑶, 漆莲芝, 张谊. 基于Pignistic概率转换和奇异值分解的证据冲突度量方法[J]. 通信学报, 2021, 42(4): 150-157.
[3]	代晓丽, 刘世峰, 宫大庆. 基于NLP的文本相似度检测方法[J]. 通信学报, 2021, 42(10): 173-181.
[4]	杨晓萍,廉伟健,李孟杰,钱志鸿. 基于Pignistic概率函数和相关系数的证据组合方法[J]. 通信学报, 2019, 40(3): 73-79.
[5]	孙贵东,关欣,衣晓,赵静. 冲突证据的相关系数度量方法[J]. 通信学报, 2018, 39(12): 30-39.
[6]	朱京伟,王晓丹,宋亚飞,黄文龙. 基于幂Pignistic概率距离的加权证据组合方法[J]. 通信学报, 2018, 39(1): 117-125.
[7]	秦丹阳,贾爽,杨松祥,马静雅,张岩,丁群. 基于信任感知的无线传感器网络安全路由机制研究[J]. 通信学报, 2017, 38(10): 60-70.
[8]	王路,邢清华,毛艺帆. 基于信任度和确定度的证据加权组合方法[J]. 通信学报, 2017, 38(1): 83-88.
[9]	王路,邢清华,毛艺帆. 单向证据冲突度量方法[J]. 通信学报, 2016, 37(7): 118-123.
[10]	王兴茂,张兴明,邬江兴. 基于一跳信任模型的协同过滤推荐算法[J]. 通信学报, 2015, 36(6): 193-200.
[11]	蒋黎明,刘志明,张琨,徐建,张宏. 基于动态分组的开放分布系统信任度量与管理研究[J]. 通信学报, 2015, 36(1): 100-110.
[12]	刘卓超,杨力,姜奇,王巍,曹春杰. 基于信任评估的Ad Hoc网络关键节点选取算法[J]. 通信学报, 2014, 35(Z2): 213-219.
[13]	刘卓超，杨力，姜奇，王巍，曹春杰. 基于信任评估的Ad Hoc网络关键节点选取算法[J]. 通信学报, 2014, 35(Z2): 29-219.
[14]	宋亚飞, 王晓丹, 雷蕾, 薛爱军. 基于相关系数的证据冲突度量方法[J]. 通信学报, 2014, 35(5): 13-100.
[15]	宋亚飞,王晓丹,雷蕾,薛爱军. 基于相关系数的证据冲突度量方法[J]. 通信学报, 2014, 35(5): 95-100.