基于规范分解的证据合成悖论分析
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摘要
利用Dempster合成规则组合证据时,有可能会出现合成悖论,且其表现形式多样,很难直接获得它们之间的规律或关系.对此,利用规范分解法将证据的基本信任分配转换为一组广义简单支持函数的组合形式.从2个典型反例分析入手,得出它们都存在信任忽略这一共同问题,在此基础上进一步总结出了Ⅰ类和Ⅱ类2种信任忽略形式及其发生的规律.对Ⅱ类信任忽略进一步分析,给出了不会发生Ⅱ类信任忽略的一般性结论.为更合理地使用Dempster合成规则避免出现合成悖论提供了依据,也为更有效地改进证据组合方法提供了参考.
When applying Dempster's rule of combination to fuse pieces of evidence,a combination paradox can occur. It is very difficult to acquire the law or relationship among these combination paradoxes with some different manifestations. In order to resolve this problem,the study is carried out by the aid of canonical decomposition which is used to transform the basic belief assignment into the combination of a set of generalized simple support function. Firstly,two typical counterexamples are analyzed,and then the common characteristic between them,neglecting belief,is summarized. On the basis of this,a further analysis is made. Two forms of neglecting belief and the rules of causing them are generalized. A further analysis of type Ⅱ neglecting belief is made. Some general conclusions,that type Ⅱ neglecting belief cannot occur,are presented. These generalized rules and conclusions provide not only the basis for applying Dempster's rule more reasonably to avoid combination paradoxes,but also the reference for modifying the combination method more effectively.
When applying Dempster's rule of combination to fuse pieces of evidence,a combination paradox can occur. It is very difficult to acquire the law or relationship among these combination paradoxes with some different manifestations. In order to resolve this problem,the study is carried out by the aid of canonical decomposition which is used to transform the basic belief assignment into the combination of a set of generalized simple support function. Firstly,two typical counterexamples are analyzed,and then the common characteristic between them,neglecting belief,is summarized. On the basis of this,a further analysis is made. Two forms of neglecting belief and the rules of causing them are generalized. A further analysis of type Ⅱ neglecting belief is made. Some general conclusions,that type Ⅱ neglecting belief cannot occur,are presented. These generalized rules and conclusions provide not only the basis for applying Dempster's rule more reasonably to avoid combination paradoxes,but also the reference for modifying the combination method more effectively.
引文
[1]Dempster A P. Upper and lower probabilities induced by a multivalued mapping[J]. Annuals of Mathematical Statistics,1967,38(2):325-339.
[2]Shafer G. A mathematical theory of evidence[M]. Princeton:Princeton University Press,1976:3-69.
[3]闫涛,赵文俊,胡秀洁,等.基于信息融合技术的航空电子设备故障诊断研究[J].电子科技大学学报,2015,44(3):392-396.Yan Tao,Zhao Wenjun,Hu Xiujie,et al. Fault diagnosis of avionic devices based on information fusion technology[J]. Journal of University of Electronic Science and Technology of China,2015,44(3):392-396.
[4]袁杰,王福利,王姝,等.基于D-S融合的混合专家知识系统故障诊断方法[J].自动化学报,2017,43(9):1580-1587.Yuan Jie,Wang Fuli,Wang Shu,et al. A fault diagnosis approach by D-S fusion theory and hybrid expert knowledge system[J]. Acta Automatica Sinica,2017,43(9):1580-1587.
[5]周俊静,段建民.基于栅格地图的智能车辆运动目标检测[J].系统工程与电子技术,2015,37(2):436-442.Zhou Junjing,Duan Jianmin. Moving object detection for in elligent vehicles based on occupancy grid map[J].Systems Engineering and Electronics,2015,37(2):436-442.
[6]杨欣,沈雷,费树岷,等.基于证据理论和多核函数融合的目标跟踪[J].东南大学学报(自然科学版),2015,45(5):861-864.Yang Xin,Shen Lei,Fei Shumin,et al. Target tracking method based on evidence theory and multiple kernel function[J]. Journal of Southeast University(Natural Science Edition),2015,45(5):861-864.
[7]郭贤生,陆浩然,王建军,等.基于证据理论的群指纹融合室内定位方法[J].电子科技大学学报,2017,46(5):654-659,665.Guo Xiansheng,Lu Haoran,Wang Jianjun,et al. A new indoor localization algorithm via Dampster-Shafer by fusing group of fingerprints evidence theory[J]. Journal of University of Electronic Science and Technology of China,2017,46(5):654-659,665.
[8]王俊华,左祥麟,左万利.基于证据理论的单词语义相似度度量[J].自动化学报,2015,41(6):1173-1186.Wang Junhua,Zuo Xianglin,Zuo Wanli. Word semantic similarity measurement based on evidence theory[J].Acta Automatica Sinica,2015,41(6):1173-1186.
[9]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.
[10]Dezert J,Wang P,Tchamova A. On the validity of Dempster-Shafer theory[C]∥Proceedings of the 15th International Conference on Information Fusion. Singapore:[s. n.],2012:655-660.
[11]Smets P. Analyzing the combination of conflicting belief functions[J]. Information Fusion,2007,8(4):387-412.
[12]Florea M C,Jousselme A L,Bosse E,et al. Robust combination rules for evidence theory[J]. Information Fusion,2009,10(2):183-197.
[13]Lefevre E,Elouedi Z. How to preserve the conflict as an alarm in the combination of belief functions[J]. Decision Support Systems,2013,56:326-333.
[14]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 Yong,Shi Wenkang. A modified combination rule of evidence theory[J]. Journal of Shanghai Jiaotong University,2003,37(8):1275-1278.
[15]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 Xin,Mu Longhua. Evidence combination rule based on local conflict elimination[J]. Systems Engineering and Electronics,2016,38(7):1594-1599.
[16]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 Changxi,Zhou Yan,Wang Shengchao,et al. A novel combination rule of evidence theory in multi-source information fusion[J]. Journal of Shanghai Jiaotong University,2016,50(7):1125-1131.
[17]薛大为,王永,高康凯.利用奇异值和虚假度的证据组合方法[J].北京邮电大学学报,2018,41(1):95-102.Xue Dawei,Wang Rong,Gao Kangkai. Evidence combination method based on singular value and falsity[J].Journal of Beijing University of Posts and Telecommunications,2018,41(1):95-102.
[18]周哲,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 Zhe,Xu Xiaobin,Wen Chenglin,et al. An optimal method for combining conflicting evidences[J].Acta Automatica Sinica,2012,38(6):976-985.
[19]杨风暴,王肖霞. D-S证据理论的冲突证据合成方法[M].北京:国防工业出版社,2010:30-80.
[20]Smets P. The canonical decomposition of a weighted belief[C]∥The 14thInternational Joint Conference on Artificial Intelligence. San Mateo:ACM,1995:1896-1901.
[2]Shafer G. A mathematical theory of evidence[M]. Princeton:Princeton University Press,1976:3-69.
[3]闫涛,赵文俊,胡秀洁,等.基于信息融合技术的航空电子设备故障诊断研究[J].电子科技大学学报,2015,44(3):392-396.Yan Tao,Zhao Wenjun,Hu Xiujie,et al. Fault diagnosis of avionic devices based on information fusion technology[J]. Journal of University of Electronic Science and Technology of China,2015,44(3):392-396.
[4]袁杰,王福利,王姝,等.基于D-S融合的混合专家知识系统故障诊断方法[J].自动化学报,2017,43(9):1580-1587.Yuan Jie,Wang Fuli,Wang Shu,et al. A fault diagnosis approach by D-S fusion theory and hybrid expert knowledge system[J]. Acta Automatica Sinica,2017,43(9):1580-1587.
[5]周俊静,段建民.基于栅格地图的智能车辆运动目标检测[J].系统工程与电子技术,2015,37(2):436-442.Zhou Junjing,Duan Jianmin. Moving object detection for in elligent vehicles based on occupancy grid map[J].Systems Engineering and Electronics,2015,37(2):436-442.
[6]杨欣,沈雷,费树岷,等.基于证据理论和多核函数融合的目标跟踪[J].东南大学学报(自然科学版),2015,45(5):861-864.Yang Xin,Shen Lei,Fei Shumin,et al. Target tracking method based on evidence theory and multiple kernel function[J]. Journal of Southeast University(Natural Science Edition),2015,45(5):861-864.
[7]郭贤生,陆浩然,王建军,等.基于证据理论的群指纹融合室内定位方法[J].电子科技大学学报,2017,46(5):654-659,665.Guo Xiansheng,Lu Haoran,Wang Jianjun,et al. A new indoor localization algorithm via Dampster-Shafer by fusing group of fingerprints evidence theory[J]. Journal of University of Electronic Science and Technology of China,2017,46(5):654-659,665.
[8]王俊华,左祥麟,左万利.基于证据理论的单词语义相似度度量[J].自动化学报,2015,41(6):1173-1186.Wang Junhua,Zuo Xianglin,Zuo Wanli. Word semantic similarity measurement based on evidence theory[J].Acta Automatica Sinica,2015,41(6):1173-1186.
[9]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.
[10]Dezert J,Wang P,Tchamova A. On the validity of Dempster-Shafer theory[C]∥Proceedings of the 15th International Conference on Information Fusion. Singapore:[s. n.],2012:655-660.
[11]Smets P. Analyzing the combination of conflicting belief functions[J]. Information Fusion,2007,8(4):387-412.
[12]Florea M C,Jousselme A L,Bosse E,et al. Robust combination rules for evidence theory[J]. Information Fusion,2009,10(2):183-197.
[13]Lefevre E,Elouedi Z. How to preserve the conflict as an alarm in the combination of belief functions[J]. Decision Support Systems,2013,56:326-333.
[14]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 Yong,Shi Wenkang. A modified combination rule of evidence theory[J]. Journal of Shanghai Jiaotong University,2003,37(8):1275-1278.
[15]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 Xin,Mu Longhua. Evidence combination rule based on local conflict elimination[J]. Systems Engineering and Electronics,2016,38(7):1594-1599.
[16]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 Changxi,Zhou Yan,Wang Shengchao,et al. A novel combination rule of evidence theory in multi-source information fusion[J]. Journal of Shanghai Jiaotong University,2016,50(7):1125-1131.
[17]薛大为,王永,高康凯.利用奇异值和虚假度的证据组合方法[J].北京邮电大学学报,2018,41(1):95-102.Xue Dawei,Wang Rong,Gao Kangkai. Evidence combination method based on singular value and falsity[J].Journal of Beijing University of Posts and Telecommunications,2018,41(1):95-102.
[18]周哲,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 Zhe,Xu Xiaobin,Wen Chenglin,et al. An optimal method for combining conflicting evidences[J].Acta Automatica Sinica,2012,38(6):976-985.
[19]杨风暴,王肖霞. D-S证据理论的冲突证据合成方法[M].北京:国防工业出版社,2010:30-80.
[20]Smets P. The canonical decomposition of a weighted belief[C]∥The 14thInternational Joint Conference on Artificial Intelligence. San Mateo:ACM,1995:1896-1901.