基于集合覆盖模型的冲突证据合成
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摘要
针对D-S证据理论在处理冲突证据时可能会造成处理结果与我们的直觉相悖的情况,在已有研究的基础上,运用集合覆盖理论,用几个非冲突子信息系统覆盖原来的带有冲突证据的信息系统,再利用D-S证据理论对每个子信息系统进行合成.最后利用概念支撑的思想定义了每个子系统的权重,合成最终的概率指派函数.所用的基于集合覆盖模型的冲突证据合成(combination of confilicting evidence based on set covering model,CCEM)的方法是对Dempeter定义组合规则的一种扩展.
In dealing with conflict evidence,D-S evidence theory might make the result and our intuition counter. The objective was to solve a problem by using the existing research and set covering model. The original information system with conflicting evidence was transformed into several sub-not-conflicting information systems. And then,it was used D-S evidence theory to fuse each sub information system. The idea of conceptual support was used to give the weights of each subsystem and get the final probability assignment function. This method was called combination of conflicting evidence based on set covering model( CCEM). It was worth noting that the method was an extension of the definition of Dempeter's combination rules.
In dealing with conflict evidence,D-S evidence theory might make the result and our intuition counter. The objective was to solve a problem by using the existing research and set covering model. The original information system with conflicting evidence was transformed into several sub-not-conflicting information systems. And then,it was used D-S evidence theory to fuse each sub information system. The idea of conceptual support was used to give the weights of each subsystem and get the final probability assignment function. This method was called combination of conflicting evidence based on set covering model( CCEM). It was worth noting that the method was an extension of the definition of Dempeter's combination rules.
引文
[1]于洪,陈云.基于Spark的三支聚类集成方法[J].郑州大学学报(理学版),2018,50(1):20-26.
[2] DEMPSTER A P. Upper and lower probabilities induced by a multivalued mapping[J]. Annals of mathematical statistics,1967,38(2):325-339.
[3] SHAFER G. A mathematical theory of evidence[M]. Princeton University:Princeton University Press,1900.
[4] DEMPSTER A P. A generalization of bayesian inference[J]. Journal of the royal statistical society,1968,30(2):205-245.
[5] ZADEH L A. Review of Shafer's mathematical theory of evidence[J]. AI magazine,1984,5(3):205-245.
[6]蒋黎明,何加浪,张宏. D-S证据理论中一种新的冲突证据融合方法[J].计算机科学,2011,38(4):236-238.
[7] QIAN J,GUO X F,DENG Y. A novel method for combining conflicting evidences based on information entropy[J]. Applied in-telligence,2017,46(4):876-888.
[8] YAGER R. On the dempster-shafer framework and new combination rules[J]. Information sciences,1987,41(2):93-137.
[9] MURPHY C K. Combining belief functions when evidence conflicts[J]. Decision support systems,2000,29(1):1-9.
[10] DUBOIS D,PRADE H. Representation and combination of uncertainty with belief functions and possibility measures[J]. Com-putational intelligence,2010,4(3):244-264.
[11] CAPRARA A,TOTH P,FISCHETTI M. Algorithms for the set covering problem[J]. Annals of operations research,2000,98(1):353-371.
[12]陈彩云,李治国.关于属性约简和集合覆盖问题的探讨[J].计算机工程与应用,2004,40(2):44-46.
[13] AKOWSKI W. Approximations in the space(U,Π)[J]. Demonstratio mathematica,1983,16(40):761-769.
[14]钱进.多粒度决策粗糙集模型研究[J].郑州大学学报(理学版),2018,50(1):33-38.
[15]徐久成,穆辉宇,冯森.基于PCA和多邻域粗糙集的肿瘤特征基因选择算法[J].郑州大学学报(理学版),2017,49(4):28-33.
[16] TAN A H,WU W Z,TAO Y Z. A set-cover-based approach for the test-cost-sensitive attribute reduction problem[J]. Softcomputing,2017,21(20):6159-6173.
[17]王丽娟,吴陈,杨习贝,等.邻域系统粗糙集和覆盖粗糙集[J].计算机科学,2013,40(1):221-224.
[18] WU W Z,QIAN Y H,LI T J,et al. On rule acquisition in incomplete multi-scale decision tables[J]. Information science,2017,378:282-302.
[19]张文修,梁怡,吴伟志.信息系统与知识发现[M].北京:科学出版社,2003.
[20]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.
[21]张文修,梁怡,徐萍.基于包含度的不确定性推理[M].北京:清华大学出版社,2005.
[2] DEMPSTER A P. Upper and lower probabilities induced by a multivalued mapping[J]. Annals of mathematical statistics,1967,38(2):325-339.
[3] SHAFER G. A mathematical theory of evidence[M]. Princeton University:Princeton University Press,1900.
[4] DEMPSTER A P. A generalization of bayesian inference[J]. Journal of the royal statistical society,1968,30(2):205-245.
[5] ZADEH L A. Review of Shafer's mathematical theory of evidence[J]. AI magazine,1984,5(3):205-245.
[6]蒋黎明,何加浪,张宏. D-S证据理论中一种新的冲突证据融合方法[J].计算机科学,2011,38(4):236-238.
[7] QIAN J,GUO X F,DENG Y. A novel method for combining conflicting evidences based on information entropy[J]. Applied in-telligence,2017,46(4):876-888.
[8] YAGER R. On the dempster-shafer framework and new combination rules[J]. Information sciences,1987,41(2):93-137.
[9] MURPHY C K. Combining belief functions when evidence conflicts[J]. Decision support systems,2000,29(1):1-9.
[10] DUBOIS D,PRADE H. Representation and combination of uncertainty with belief functions and possibility measures[J]. Com-putational intelligence,2010,4(3):244-264.
[11] CAPRARA A,TOTH P,FISCHETTI M. Algorithms for the set covering problem[J]. Annals of operations research,2000,98(1):353-371.
[12]陈彩云,李治国.关于属性约简和集合覆盖问题的探讨[J].计算机工程与应用,2004,40(2):44-46.
[13] AKOWSKI W. Approximations in the space(U,Π)[J]. Demonstratio mathematica,1983,16(40):761-769.
[14]钱进.多粒度决策粗糙集模型研究[J].郑州大学学报(理学版),2018,50(1):33-38.
[15]徐久成,穆辉宇,冯森.基于PCA和多邻域粗糙集的肿瘤特征基因选择算法[J].郑州大学学报(理学版),2017,49(4):28-33.
[16] TAN A H,WU W Z,TAO Y Z. A set-cover-based approach for the test-cost-sensitive attribute reduction problem[J]. Softcomputing,2017,21(20):6159-6173.
[17]王丽娟,吴陈,杨习贝,等.邻域系统粗糙集和覆盖粗糙集[J].计算机科学,2013,40(1):221-224.
[18] WU W Z,QIAN Y H,LI T J,et al. On rule acquisition in incomplete multi-scale decision tables[J]. Information science,2017,378:282-302.
[19]张文修,梁怡,吴伟志.信息系统与知识发现[M].北京:科学出版社,2003.
[20]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.
[21]张文修,梁怡,徐萍.基于包含度的不确定性推理[M].北京:清华大学出版社,2005.