A Combination Rule of Evidence Theory Based on Similarity of Focal Elements
YANG Shan-Lin1,2, LUO He1,2,3, HU Xiao-Jian1,2
1.Institute of Computer Network and System, Hefei University of Technology, Hefei 230009 2.Key Laboratory of Ministry of Education on Process Optimization & Intelligent Decision Making, School of Management, Hefei University of Technology, Hefei 230009 3.School of Computer and Information, Hefei University of Technology, Hefei 230009
Abstract Aiming at the problems of irrational assignment of conflict evidence, one-vote negation and poor robustness in evidence combination, a combination rule is proposed based on the notion of the similarity of focal elements and the distances between focal elements. The process of combination is divided into two parts, combination with and without conflicted mass. The mathematical proof of the proposed combination rule is presented, and the comparative experiments are conducted. The results show that the proposed rule can assign the conflicted mass rationally and avoid one-vote negation with good robustness.
[1] Waltz E, Llinas J. Multisensor Data Fusion. Boston, USA: Artech House, 1990 [2] Dempster A P. Upper and Lower Probabilities Induced by a Multivalued Mapping. The Annals of Mathematical Statistics, 1967, 38(2): 325-339 [3] Shafer G. A Mathematical Theory of Evidence. Princeton, USA: Princeton University Press, 1967 [4] Yager R R. On the Dempster-Shafer Framework and New Combination Rules. Information Sciences: An International Journal, 1987, 41(2): 93-137 [5] Smets P. The Combination of Evidence in the Transferable Belief Model. IEEE Trans on Pattern Analysis and Machine Intelligence, 1990, 12(5): 447-458 [6] Lefevre E, Colot O, Vannoorenberghe P. Belief Functions Combination and Conflict Management. Information Fusion, 2002, 3(2):149-162 [7] Sun Quan, Ye Xiuqing, Gu Weikang. A New Combination Rules of Evidence Theory. Acta Electronica Sinica, 2000, 28(8): 117-119 (in Chinese) (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) [8] He Bing, Hao Aimin, Zhao Qinping. A Decision Making Method Based on Uncertain Information. Chinese Journal of Computers, 2004, 27(2): 281-285 (in Chinese) (何 兵,郝爱民,赵沁平.一种基于不确定信息的决策方法.计算机学报, 2004, 27(2): 281-285) [9] Xu Lingyu, Zhang Bofeng, Xu Weimin, et al. Evidence Ullage Analysis in D-S Theory and Development. Journal of Software, 2004, 15(1): 69-75 (in Chinese) (徐凌宇,张博锋,徐炜民,等.D-S理论中证据损耗分析及改进方法.软件学报, 2004, 15(1): 69-75) [10] Joussleme A L, Grenier D, Bosse E. A New Distance between Two Bodies of Evidence. Information Fusion, 2001, 2(2): 91-101 [11] Wang Wenjie, Ye Shiwei. Theory and Application of Artificial Intelligence. Beijing, China: Posts & Telecom Press, 2004 (in Chinese) (王文杰,叶世伟.人工智能原理与应用.北京:人民邮电出版社, 2004) [12] Deng Yong, Shi Wenkang, Zhu Zhenfu, et al. Combining Belief Functions Based on Distance of Evidence. Decision Support Systems, 2004, 38(3): 489-493 [13] Lin Zhigui, Xu Lizhong, Zhou Jinling. The Combination Method of Conflict Evidence Based on Modified Model. Journal of Shanghai Jiaotong University, 2006, 40(11): 1964-1970 (in Chinese) (林志贵,徐立中,周金陵.基于修改模型的冲突证据组合方法.上海交通大学学报, 2006, 40(11): 1964-1970) [14] Pan Quan, Zhang Shanying, Cheng Yongmei, et al. Some Research on Robustness of Evidence Theory. Acta Automatica Sinica, 2001, 27(6): 798-805 (in Chinese) (潘 泉,张山鹰,程咏梅,等.证据推理的鲁棒性研究.自动化学报, 2001, 27(6): 798-805) [15] Liu Dayou, Yang Kun, Tang Haiying, et al. A Convex Evidence Theory Model. Journal of Computer Research and Development, 2000, 37(2): 175-181 (in Chinese) (刘大有,杨 鲲,唐海鹰,等.凸函数证据理论模型.计算机研究与发展, 2000, 37(2): 175-181) [16] Liu Weiru. Analyzing the Degree of Conflict among Belief Functions. Artificial Intelligence, 2006, 170(11): 909-924
2009, Vol. 22 
