An Optimal Method for Combining Conflicting Evidences
-
摘要: 多数研究者认为, 用修改数据模型(证据体)的方法来解决冲突证据组合问题较为合理. 然而, 已有的基于修改数据模型的方法仅考虑如何提高冲突证据组合结果的聚焦程度. 实际上, 它们并没有考虑如何通过修正来消减证据之间的冲突. 显然, 若融合结果由冲突证据组合得到, 那么其可信性必然较低且会给随后的融合过程带来较大的风险. 针对此问题, 沿用折扣系数法, 该文基于证据距离准则提出了一种折扣系数(可靠度)优化学习模型, 优化过程同时考虑提高聚焦程度和消减冲突, 通过使折扣修正后组合结果的基本概率赋值(Basic probability assignment, BPA)与直言BPA (Categorical BPA, CBPA)之间的距离最小来寻优, 其中证据可靠度大小的序关系作为约束条件, 它依据证据的虚假度确定. 典型算例验证了所提方法比现有的一些组合方法, 在聚焦能力和冲突消减两方面都更合理.Abstract: Most researchers hold that revising mass function based methods are reasonable to deal with the problem of conflicting evidence combination. However, the existing methods of revising mass function only consider improving focusing degree of combination results. Actually, they did not effectively reduce conflict among evidences by revision. Obviously, the fusion result of conflicting evidences has low credibility and will certainly bring risks to subsequent fusion process. To solve this problem, by adopting the idea of discounting, this paper proposes an optimal model to learn discounting factors (reliability) based on evidence distance criterion which considers improving focusing degree and reducing conflict simultaneously. The procedures of optimization are achieved through minimizing the distance between combined basic probability assignment (BPA) of revised mass function and categorical BPA (CBPA). The permutation of reliabilities associated with evidences, which is regarded as constraint condition, is determined according to their falsity. Typical examples illustrate that the presented method is more reasonable than some existing methods both in reducing conflict and improving focusing degree.
-
Key words:
- Information fusion /
- evidence theory /
- conflict /
- falsity /
- optimization
-
[1] Dempster A P. Upper and lower probabilities induced by a multivalued mapping. Annual Mathematics and Statistics, 1967, 38(2): 325-339[2] Shafer G. A Mathematical Theory of Evidence. NJ: Princeton University Press, 1976[3] Li Peng, Liu Si-Feng. Interval-valued intuitionistic fuzzy numbers decision-making method based on grey incidence analysis and D-S theory of evidence. Acta Automatica Sinica, 2011, 37(8): 993-998 (李鹏, 刘思峰. 基于灰色关联分析和 D-S 证据理论的区间直觉模糊决策方法. 自动化学报, 2011, 37(8): 993-998)[4] Wen Cheng-Lin, Zhou Zhe, Xu Xiao-Bin. A new similarity measure between generalized trapezoidal fuzzy numbers and its application to fault diagnosis. Acta Electronica Sinica, 2011, 39(3A): 1-6 (文成林, 周哲, 徐晓滨. 一种新的广义梯形模糊数相似性度量方法及在故障诊断中的应用. 电子学报, 2011, 39(3A): 1-6)[5] Zadeh L A. A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination. AI Magazine, 1986, 7(2): 85-90[6] Smets P. The combination of evidence in the transferable belief model. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990, 12(5): 447-458[7] Yager R R. On the Dempster-Shafer framework and new combination rules. Information Science, 1987, 41(2): 93- 137[8] Deng Yong, Shi Wen-Kang. A modified combination rule of evidence theory. Journal of Shanghai Jiaotong University, 2003, 37(8): 1275-1278 (邓勇, 施文康. 一种改进的证据推理组合规则. 上海交通大学学报, 2003, 37(8): 1275-1278)[9] Sun Quan, Ye Xiu-Qing, Gu Wei-Kang. A new combination rules of evidence theory. Acta Electronica Sinica, 2000, 28(8): 117-119 (孙全, 叶秀清, 顾伟康. 一种新的基于证据理论的合成公式. 电子学报, 2000, 28(8): 117-119)[10] Lefévre E, Colot O, Vannoorenberghe P. Belief function combination and conflict management. Information Fusion, 2002, 3(2): 149-162[11] Dubois D, Prade H. A set-theoretic view of belief functions: logical operations and approximations by fuzzy sets. International Journal of General Systems, 1986, 12(3): 193-226[12] Dambreville F, Celeste F, Dezert J, Smarandache F. Probabilistic PCR6 fusion rule. Advances and Applications and Advances of DSmT for Information Fusion, Rehoboth: American Research Press, 2009, 3: 137-160[13] Haenni R. Are alternatives to Dempster's rule of combination real alternative? Comments on ''About the belief function combination and the conflict management problem'' --- Lefévre et al. Information Fusion, 2002, 3(3): 237-239[14] Murphy C K. Combining belief functions when evidence conflicts. Decision Support Systems, 2000, 29(1): l-9[15] Deng Y, Shi W K, Zhu Z F, Liu Q. Combining belief functions based on distance of evidence. Decision Support Systems, 2004, 38(3): 489-493[16] Hu Chang-Hua, Si Xiao-Sheng, Zhou Zhi-Jie, Wang Peng. An improved D-S algorithm under the new measure criteria of evidence conflict. Acta Electronica Sinica, 2009, 37(7): 1578-1583 (胡昌华, 司小胜, 周志杰, 王鹏. 新的证据冲突衡量标准下的DS改进算法. 电子学报, 2009, 37(7): 1578-1583)[17] Smets P. Analyzing the combination of conflicting belief functions. Information Fusion, 2007, 8(4): 378-412[18] Liu W R. Analyzing the degree of conflict among belief functions. Artificial Intelligence, 2006, 170(11): 909-924[19] Jiang Wen, Zhang An, Deng Yong. A novel information fusion method based on our evidence conflict representation. Journal of Northwestern Polytechnical University, 2010, 28(1): 27-32 (蒋雯, 张安, 邓勇. 基于新的证据冲突表示的信息融合方法研究. 西北工业大学学报, 2010, 28(1): 27-32)[20] Schubert J. Conflict management in Dempster-Shafer theory using the degree of falsity. International Journal of Approximate Reasoning, 2011, 52(3): 449-460[21] Jousselme A L, Grenier D, Bossé . A new distance between two bodies of evidence. Information Fusion, 2001, 2(2): 91-101[22] Guo K H, Li W L. Combination rule of D-S evidence theory based on the strategy of cross merging between evidences. Expert Systems with Applications, 2011, 38(10): 13360-13366
点击查看大图
计量
- 文章访问数: 2713
- HTML全文浏览量: 91
- PDF下载量: 890
- 被引次数: 0