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冲突证据决策新方法及应用

赵静 关欣 刘海桥

赵静, 关欣, 刘海桥等 . 冲突证据决策新方法及应用[J]. 北京航空航天大学学报, 2019, 45(9): 1838-1847. doi: 10.13700/j.bh.1001-5965.2018.0787
引用本文: 赵静, 关欣, 刘海桥等 . 冲突证据决策新方法及应用[J]. 北京航空航天大学学报, 2019, 45(9): 1838-1847. doi: 10.13700/j.bh.1001-5965.2018.0787
ZHAO Jing, GUAN Xin, LIU Haiqiaoet al. A new conflict evidence decision method and its application[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(9): 1838-1847. doi: 10.13700/j.bh.1001-5965.2018.0787(in Chinese)
Citation: ZHAO Jing, GUAN Xin, LIU Haiqiaoet al. A new conflict evidence decision method and its application[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(9): 1838-1847. doi: 10.13700/j.bh.1001-5965.2018.0787(in Chinese)

冲突证据决策新方法及应用

doi: 10.13700/j.bh.1001-5965.2018.0787
基金项目: 

国家自然科学基金 91538201

国家自然科学基金 61671463

国家自然科学基金 61571454

国防科技卓越青年科学基金 2017-JCJQ-2Q-003

泰山学者工程 ts201712072

详细信息
    作者简介:

    赵静  女, 博士研究生。主要研究方向:不确定推理、目标识别

    关欣  女, 博士, 教授, 博士生导师。主要研究方向:信息对抗、目标跟踪与识别

    刘海桥  男, 硕士研究生。主要研究方向:不确定推理、目标识别

    通讯作者:

    关欣, E-mail: 597268914@qq.com

  • 中图分类号: TN95;C934

A new conflict evidence decision method and its application

Funds: 

National Natural Science Foundation of China 91538201

National Natural Science Foundation of China 61671463

National Natural Science Foundation of China 61571454

National Defense Science and Technology Excellence Youth Talent Fund 2017-JCJQ-2Q-003

Taishan Scholar Engineering Special Fund ts201712072

More Information
  • 摘要:

    冲突证据决策方法研究是证据理论重要研究课题。鉴于现有的证据理论改进方法在冲突证据决策过程中存在计算量较大,归一化过程不合理,证据组合效果不理想等一系列问题,提出基于二次组合的冲突证据决策方法。首先,提出新的基于二次组合的冲突证据决策方法的流程图;然后,提出新的乘性归一化规则,并对新的乘性归一化规则进行算例分析,验证其合理性;最后,分析现有冲突度量函数的不足,并提出新的冲突度量函数,并分析冲突度量函数的合理性。通过算例分析,并与现有证据组合规则的比较表明,所提方法不仅计算量得以改善,组合结果也得到提升。

     

  • 图 1  折扣证据组合模型

    Figure 1.  Discount evidence combination model

    图 2  基于二次组合的冲突证据决策模型

    Figure 2.  Conflict evidence decision model based on quadratic combination

    图 3  预处理误差

    Figure 3.  Preprocessing error

    图 4  基于Jousselme距离和二次组合的冲突证据决策计算量图

    Figure 4.  Graph of calculated amount of conflict evidence decision based on Jousselme distance and quadratic combination

    图 5  基于Jousselme距离和二次组合的冲突证据决策计算量的对数图

    Figure 5.  Graph of logarithm of calculated amount of conflict evidence based on Jousselme distance and quadratic combination

    表  1  加性与乘性归一化折扣证据组合结果

    Table  1.   Additive and multiplicative normalized discount evidence combination results

    组合规则 mi(A) mi(B) mi(AB) mi(C) mi(AC) mi(BC) mi(ABC)
    PCR6 0.5436 0.0939 0.0403 0.2544 0.0224 0.0454 0
    PCR6+ 0.5386 0.0938 0.0314 0.0588 0.0095 0.0205 0.2475
    PCR6× 0.6379 0.0751 0.0622 0.0523 0.0641 0.1083 0
    下载: 导出CSV

    表  2  证据组BPAs

    Table  2.   Evidence group BPAs

    mi(·) BPA
    A B AB C AC BC ABC
    m1 0.7 0.1 0.1 0.1 0 0 0
    m2 0.6 0.2 0 0.1 0 0 0.1
    m3 0.6 0.05 0 0.05 0 0 0.3
    m4 0.4 0.3 0 0.2 0.1 0 0
    m5 0.1 0.7 0 0.1 0 0 0.1
    m6 0.9 0.05 0 0.05 0 0 0
    下载: 导出CSV

    表  3  折扣证据组BPAs

    Table  3.   Discounted evidence group BPAs

    mi′(·) BPA
    A B AB C AC BC ABC
    m1 0.74 0.11 0.04 0.11 0 0 0
    m2 0.64 0.21 0 0.11 0 0 0.05
    m3 0.72 0.06 0 0.06 0 0 0.16
    m4 0.40 0.30 0 0.20 0.10 0 0
    m5 0.03 0.21 0 0.03 0 0 0.73
    m6 0.90 0.05 0 0.05 0 0 0
    下载: 导出CSV

    表  4  算例不同组合规则计算结果

    Table  4.   Calculation results of different combination rules of example

    组合规则 mi(A) mi(B) mi(AB) mi(C) mi(AC) mi(BC) mi(ABC)
    PCR1 0.57 0.22 0.02 0.10 0.02 0 0.08
    PCR2 0.57 0.22 0.02 0.10 0.02 0 0.08
    PCR3 0.67 0.24 0 0.06 0 0 0.04
    PCR5 0.46 0.35 0.01 0.07 0.01 0 0.10
    PCR6 0.72 0.21 0 0.03 0 0 0.04
    本文方法 0.77 0.07 0 0.02 0 0 0.14
    下载: 导出CSV
  • [1] DEMPSTER A P.Upper and lower probabilities induced by a multivalued mapping[J].Annals of Mathematical Statistics, 1967, 38(2):325-339. doi: 10.1214/aoms/1177698950
    [2] SHAFER G.A mathematical theory of evidence[M].Princeton:Princeton University Press, 1976:85-150.
    [3] XU Z, HU C, YANG F, et al.Data-driven inter-turn short circuit fault detection in induction machines[J].IEEE Access, 2017, 5:25055-25068. doi: 10.1109/ACCESS.2017.2764474
    [4] WANG X, YANG F, WEI H, et al.A risk assessment model of uncertainty system based on set-valued mapping[J].Journal of Intelligent and Fuzzy Systems, 2016, 31(6):3155-3162. doi: 10.3233/JIFS-169201
    [5] ZHANG X, MAHADEVAN S, DENG X.Reliability analysis with linguistic data:An evidential network approach[J].Reliability Engineering and System Safety, 2017, 162:111-121. doi: 10.1016/j.ress.2017.01.009
    [6] JIANG W, XIE C, ZHUANG M, et al.Failure mode and effects analysis based on a novel fuzzy evidential method[J].Applied Soft Computing, 2017, 57:672-683. doi: 10.1016/j.asoc.2017.04.008
    [7] HAN D, DEZERT J, YANG Y.Belief interval-based distance measures in the theory of belief functions[J].IEEE Transactions on Systems, Man, and Cybernetics:Systems, 2016, 99:1-18. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=bf1780050aa2931bc855837e35c9b3c4
    [8] QIAN J, GUO X F, DENG Y.A novel method for combining conflicting evidences based on information entropy[J].Applied Intelligence, 2017, 46(4):876-888. doi: 10.1007/s10489-016-0875-y
    [9] YU C, YANG J, YANG D, et al.An improved conflicting evidence combination approach based on a new supporting probability distance[J].Expert Systems with Applications, 2015, 42(12):5139-5149. doi: 10.1016/j.eswa.2015.02.038
    [10] SMARANDACHE F, DEZERT J.Modified PCR rules of combination with degrees of intersections[C]//International Conference on Information Fusion.Piscataway, NJ: IEEE Press, 2015: 2100-2107.
    [11] JIANG W, LUO Y, QIN X, et al.An improved method to rank generalized fuzzy numbers with different left heights and right heights[J].Journal of Intelligent and Fuzzy Systems, 2015, 28(5):2343-2355. doi: 10.3233/IFS-151639
    [12] JIANG W, WEI B, QIN X, et al.Sensor data fusion based on a new conflict measure[J].Mathematical Problems in Engineering, 2016, 2016:5769061.
    [13] ZADEH L A.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. http://dl.acm.org/citation.cfm?id=13443
    [14] LIU Z G, DEZERT J, PAN Q, et al.Combination of sources of evidence with different discounting factors based on a new dissimilarity measure[J].Decision Support Systems, 2011, 52(1):133-141. doi: 10.1016/j.dss.2011.06.002
    [15] MARTIN A, JOUSSELME A L, OSSWALD C.Conflict measure for the discounting operation on belief functions[C]//International Conference on Information Fusion.Piscataway, NJ: IEEE Press, 2008: 1-8.
    [16] YANG Y, HAN D, HAN C.Discounted combination of unreliable evidence using degree of disagreement[J].International Journal of Approximate Reasoning, 2013, 54(8):1197-1216. doi: 10.1016/j.ijar.2013.04.002
    [17] DENG X Y, HU Y, DENG Y, et al.Environmental impact assessment based on D numbers[J].Expert Systems with Applications, 2014, 41(2):635-643. doi: 10.1016/j.eswa.2013.07.088
    [18] FEI L G, HU Y, XIAO F Y, et al.A modified TOPSIS method based on D numbers and its applications in human resources selection[J].Mathematical Problems in Engineering, 2016, 2016:6145196. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=Doaj000004637719
    [19] BIAN T, ZHENG H Y, YIN L K, et al.Failure mode and effects analysis based on D numbers and TOPSIS[J].Knowledge-based Systems, 2016, 2016:1-39. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=fe09587832848b75d72fee89a7aaef40
    [20] SU X Y, MAHADEVAN S, XU P D, et al.Dependence assessment in human reliability analysis based on D numbers and AHP[J].Risk Analysis, 2015, 35(7):1296-1316. doi: 10.1111/risa.2015.35.issue-7
    [21] DENG X Y, HU Y, DENG Y.Supplier selection using AHP methodology extended by D numbers[J].Expert Systems with Applications, 2014, 41(1):156-167. doi: 10.1016/j.eswa.2013.07.018
    [22] FANG C, ZHONG D H, YAN F G, et al.A hybrid fuzzy evaluation method for curtain grouting efficiency assessment based on an AHP method extended by D numbers[J].Expert Systems with Applications, 2016, 44(1):289-303. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=6adcda7336749af1293cbfca2c883cb2
    [23] DENG X Y, LU X, CHAN F T, et al.D-CFPR:D numbers extended consistent fuzzy preference relations[J].Knowledge-based Systems, 2015, 73:61-68. doi: 10.1016/j.knosys.2014.09.007
    [24] ZHOU X Y, SHI Y Q Y, DENG Y, et al.D-DEMATEL:A new method to identify critical success factors in emergency management[J].Safety Science, 2017, 91:93-104. doi: 10.1016/j.ssci.2016.06.014
    [25] LIU W.Analyzing the degree of conflict among belief functions[J].Artificial Intelligence, 2006, 170(11):909-924. doi: 10.1016/j.artint.2006.05.002
    [26] KHATIBI V, MONTAZER G A.A new evidential distance measure based on belief intervals[J].Scientia Iranica, 2010, 17(2):119-132.
    [27] CHEN J, YE F, JIANG T, et al.Conflicting information fusion based on an improved DS combination method[J].Symmetry, 2017, 9(11):278. doi: 10.3390/sym9110278
    [28] HÖHLE U.Entropy with respect to plausibility measures[C]//Proceedings of the 12th IEEE International Symposium on Multiple-Valued Logic.Piscataway, NJ: IEEE Press, 1982: 167-169.
    [29] YAGER R R.Entropy and specificity in a mathematical theory of evidence[J].International Journal of General Systems, 2008, 219(4):291-310. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.1080/03081078308960825
    [30] KLIR G J, RAMER A.Uncertainty in the Dempster-Shafer theory:A critical re-examination[J].International Journal of General Systems, 1990, 18(2):155-166. doi: 10.1080/03081079008935135
    [31] KLIR G J, PARYIZ B.A note on the measure of discord[C]//8th International Conference on Uncertainty in Artificial Intelligence.San Francisco: Morgan Kaufmann Publishers Inc., 1992: 138-141.
    [32] HARMANEC D, KLIR G J.Measuring total uncertainty in Dempster-Shafer theory:A novel approach[J].International Journal of General Systems, 1994, 22(4):405-419. doi: 10.1080/03081079408935225
    [33] JOUSSELME A L, LIU C, GRENIER D, et al.Measuring ambiguity in the evidence theory[J].IEEE Transactions on Systems, Man, and Cybernetics-Part A:Systems and Humans, 2006, 36(5):890-903. doi: 10.1109/TSMCA.2005.853483
    [34] DENG Y.Deng entropy:A generalized Shannon entropy to measure uncertainty[J].Chaos, Solitons & Fractals, 2016, 91:549-553. http://www.sciencedirect.com/science/article/pii/S0960077916302363
    [35] JOUSSELME A L, GRENIER D, BOSSÉ É.A new distance between two bodies of evidence[J].Information Fusion, 2001, 2(2):91-101. doi: 10.1016/S1566-2535(01)00026-4
    [36] DING J, HAN D, DEZERT J, et al.Comparative study on BBA determination using different distances of interval numbers[C]//International Conference on Information Fusion.Piscataway, NJ: IEEE Press, 2017: 1-6.
    [37] YANG Y, HAN D, DEZERT J, et al.Comparative study of focal distance measures in theory of belief functions[C]//International Conference on Information Fusion.Piscataway, NJ: IEEE Press, 2017: 979-984.
    [38] ZHOU D, PAN Q, CHHIPI-SHRESTHA G, et al.A new weighting factor in combining belief function[J].PLOS ONE, 2017, 12(5):e0177695. doi: 10.1371/journal.pone.0177695
    [39] YANG Y, HAN D.A new distance-based total uncertainty measure in the theory of belief functions[J].Knowledge-Based Systems, 2016, 94:114-123. doi: 10.1016/j.knosys.2015.11.014
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出版历程
  • 收稿日期:  2019-01-02
  • 录用日期:  2019-03-22
  • 刊出日期:  2019-09-20

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