基于量子演化的信度函数概率转换

周千里; 邓勇

doi:10.7527/S1000-6893.2022.26947

航空学报 >

2022 , Vol. 43 >Issue S1: 726947 - 726947

DOI: https://doi.org/10.7527/S1000-6893.2022.26947

信息融合

基于量子演化的信度函数概率转换

周千里 ,
邓勇

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1. 电子科技大学基础与前沿研究院，成都 611731;
2. 陕西师范大学教育学院，西安 710062

收稿日期: 2022-01-12

修回日期: 2022-01-13

网络出版日期: 2022-11-15

基金资助

国家自然科学基金（61973332）

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Quantum-like probability transformation of belief function

ZHOU Qianli ,
DENG Yong

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1. Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu 611731, China;
2. School of Education, Shaanxi Normal University, Xi'an 710062, China

Received date: 2022-01-12

Revised date: 2022-01-13

Online published: 2022-11-15

Supported by

National Natural Science Foundation of China （61973332）

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摘要

将信度函数转换为合理的概率分布是解决信息融合、专家决策以及多目标分类问题的关键。基于量子基本信度指派（QBBA）的生成方法，构建了一种信度演化有向无环图（BEDAG），并赋予了信度函数的概率转换问题一个新的解释。在此基础上，利用量子计算中的RY旋转门来模拟QBBA的信度在BEDAG传递的过程，并提出了一种新的概率转换方法。根据概率信息容量（PIC）这一指标验证，相比之前提出的经典方法，对于相同的信度函数，该方法可以产生更高的PIC值。因此，提出的方法更适合用于不确定环境下的信息融合与决策。

关键词： Dempster-Shafer证据理论; 量子信度函数; 量子演化; 有向无环图; 概率转换

本文引用格式

周千里 , 邓勇 . 基于量子演化的信度函数概率转换[J]. 航空学报, 2022 , 43(S1) : 726947 -726947 . DOI: 10.7527/S1000-6893.2022.26947

Abstract

Transforming the belief function into a reasonable probability distribution is the key to solving the problems of information fusion， expert decision-making and multi-objective classification. In this paper， based on the generation method of Quantum Basic Belief Assignment （QBBA）， a Belief Evolution Directed Acyclic Graph （BEDAG） is constructed， and a new interpretation of probability transformation is proposed. On this basis， this paper uses the RY gate in quantum computing to simulate the process of belief evolution of QBBA in BEDAG， and proposes a new probability transformation method. According to the indicator of Probability Information Content （PIC）， for the same belief functions， the proposed method can generate higher PIC value than the classical method proposed before. Therefore， the proposed method is more suitable for information fusion and decision-making in uncertain environments.

Key words： Dempster-Shafer evidence theory; quantum belief function; quantum evolution; directed acyclic graph; probability transformation

参考文献

[1] DEMPSTER A P. Upper and lower probabilities induced by a multivalued mapping[M]∥Classic works of the Dempster-Shafer theory of belief functions. Berlin, Heidelberg: Springer, 2008: 57-72.
[2] SHAFER G. A mathematical theory of evidence[M]. Princeton: Princeton University Press, 1976.
[3] HE Y, XIONG W, LIU J, et al. Review and prospect of research on maritime information perception and fusion[J]. Fire Control & Command Control, 2018, 43(6): 1-10 (in Chinese). 何友, 熊伟, 刘俊, 等. 海上信息感知与融合研究进展及展望[J]. 火力与指挥控制, 2018, 43(6): 1-10.
[4] HE Y, HU L F, GUAN X, et al. A new method of measuring the degree of conflict among general basic probability assignments[J]. Science in China (Information Sciences), 2011, 41(8): 989-997(in Chinese). 何友, 胡丽芳, 关欣, 等. 一种度量广义基本概率赋值冲突的方法[J]. 中国科学(信息科学), 2011, 41(8): 989-997.
[5] LIU Z G, CHENG Y M, PAN Q, et al. Target identification by adaptive combination of conflicting evidence[J]. Acta Aeronautica et Astronautica Sinica, 2010, 31(7): 1426-1432 (in Chinese). 刘准钆, 程咏梅, 潘泉, 等. 证据冲突下自适应融合目标识别算法[J]. 航空学报, 2010, 31(7): 1426-1432.
[6] LIU Z G, ZHANG X X, NIU J W, et al. Combination of classifiers with different frames of discernment based on belief functions[J]. IEEE Transactions on Fuzzy Systems, 2021, 29(7): 1764-1774.
[7] SHENG W J, LI X D. Multi-task learning for gait-based identity recognition and emotion recognition using attention enhanced temporal graph convolutional network[J]. Pattern Recognition, 2021, 114: 107868.
[8] PAN Q, HU Y M, MA J R. Intelligence, surveillance and reconnaissance based on variational Bayesian joint optimization[J]. Command Information System and Technology, 2020, 11(2): 1-8 (in Chinese). 潘泉, 胡玉梅, 马季容. 基于变分贝叶斯联合优化的情报监视与侦察[J]. 指挥信息系统与技术, 2020, 11(2): 1-8.
[9] HE Y, ZHOU W. Big data technology for maritime information sensing[J]. Command Information System and Technology, 2018, 9(2): 1-7 (in Chinese). 何友, 周伟. 海上信息感知大数据技术[J]. 指挥信息系统与技术, 2018, 9(2): 1-7.
[10] GUO Q, HE Y. DSm evidence modeling and radar emitter fusion recognition method based on cloud model[J]. Journal of Electronics & Information Technology, 2015, 37(8): 1779-1785 (in Chinese). 郭强, 何友. 基于云模型的DSm证据建模及雷达辐射源识别方法[J]. 电子与信息学报, 2015, 37(8): 1779-1785.
[11] GUAN X, SUN G D, GUO Q, et al. Radar emitter parameter recognition based on interval number and evidence theory[J]. Systems Engineering and Electronics, 2014, 36(7): 1269-1274 (in Chinese). 关欣, 孙贵东, 郭强, 等. 基于区间数和证据理论的雷达辐射源参数识别[J]. 系统工程与电子技术, 2014, 36(7): 1269-1274.
[12] LIU Z G, LIU Y, DEZERT J, et al. Evidence combination based on credal belief redistribution for pattern classification[J]. IEEE Transactions on Fuzzy Systems, 2020, 28(4): 618-631.
[13] ZHOU Q L, DENG Y. Fractal-based belief entropy[J]. Information Sciences, 2022, 587: 265-282.
[14] DENG Y, JIANG W, HAN D Q. Basic frame of generalized evidence theory[J]. Journal of Xi'an Jiaotong University, 2010, 44(12): 119-124 (in Chinese). 邓勇, 蒋雯, 韩德强. 广义证据理论的基本框架[J]. 西安交通大学学报, 2010, 44(12): 119-124.
[15] HU L F, GUAN X, HE Y. Recursive target identification fusion methods based on Dezert-Smarandache theory[J]. Control Theory & Applications, 2012, 29(1): 79-84 (in Chinese). 胡丽芳, 关欣, 何友. 基于Dezert-Smarandache理论的递归目标识别融合方法[J]. 控制理论与应用, 2012, 29(1): 79-84.
[16] HU L F, GUAN X, HE Y. A new combination rule based on DSmT[J]. Fire Control and Command Control, 2009, 34(7): 9-11 (in Chinese). 胡丽芳, 关欣, 何友. 一种新的基于DSmT的合成公式[J]. 火力与指挥控制, 2009, 34(7): 9-11.
[17] LIU Z G, PAN Q, HAN D Q. A brief introduction to multi-source information fusion [J]. Scientia Sinica (Informationis), 2020, 50(11): 1781-1782 (in Chinese). 刘准钆, 潘泉, 韩德强. 多源信息融合专题简介[J]. 中国科学: 信息科学, 2020, 50(11): 1781-1782.
[18] PAN Q, WANG Z F, LIANG Y, et al. Basic methods and progress of information fusion (Ⅱ)[J]. Control Theory & Applications, 2012, 29(10): 1233-1244 (in Chinese). 潘泉, 王增福, 梁彦, 等. 信息融合理论的基本方法与进展(Ⅱ)[J]. 控制理论与应用, 2012, 29(10): 1233-1244.
[19] TESSEM B. Approximations for efficient computation in the theory of evidence[J]. Artificial Intelligence, 1993, 61(2): 315-329.
[20] LI F, LI S M, DENOEUX T. Clustering ensemble method based on belief function theory[J]. Journal of Nanjing University of Information Science & Technology (Natural Science Edition), 2019, 11(3): 332-339 (in Chinese). 李锋, 李寿梅, Denoeux Thierry. 基于证据理论的聚类集成方法[J]. 南京信息工程大学学报(自然科学版), 2019, 11(3): 332-339.
[21] WANG D, LI Q, JIANG W, et al. New method to combine conflict evidence based on pignistic probability distance[J]. Infrared and Laser Engineering, 2009, 38(1): 149-154 (in Chinese). 王栋, 李齐, 蒋雯, 等. 基于pignistic概率距离的冲突证据合成方法[J]. 红外与激光工程, 2009, 38(1): 149-154.
[22] SMETS P, KENNES R. The transferable belief model[J]. Artificial Intelligence, 1994, 66(2): 191-234.
[23] SMETS P. Decision making in the TBM: The necessity of the pignistic transformation[J]. International Journal of Approximate Reasoning, 2005, 38(2): 133-147.
[24] JIANG W, HUANG C, DENG X Y. A new probability transformation method based on a correlation coefficient of belief functions[J]. International Journal of Intelligent Systems, 2019, 34(6): 1337-1347.
[25] COBB B R, SHENOY P P. On the plausibility transformation method for translating belief function models to probability models[J]. International Journal of Approximate Reasoning, 2006, 41(3): 314-330.
[26] CUZZOLIN F. On the relative belief transform[J]. International Journal of Approximate Reasoning,2012,53(5): 786-804.
[27] HAN D Q, DEZERT J, DUAN Z S. Evaluation of probability transformations of belief functions for decision making[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2016, 46(1): 93-108.
[28] FAN H. Quantum computation and quantum simulation[J]. Acta Physica Sinica, 2018, 67(12): 16-25 (in Chinese). 范桁. 量子计算与量子模拟[J]. 物理学报, 2018, 67(12): 16-25.
[29]
[30] SHOR P W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer[J]. SIAM Review, 1999, 41(2): 303-332.
[31] DUAN B J, YUAN J B, YU C H, et al. A survey on HHL algorithm: From theory to application in quantum machine learning[J]. Physics Letters A, 2020, 384(24): 126595.
[32] HUANG Y M, LEI H, LI X Y. A survey on quantum machine learning[J]. Chinese Journal of Computers, 2018, 41(1): 145-163 (in Chinese). 黄一鸣, 雷航, 李晓瑜. 量子机器学习算法综述[J]. 计算机学报, 2018, 41(1): 145-163.
[33] LIU Z G, CHENG Y M, PAN Q, et al. Weight evidence combination for multi-sensor conflict information[J]. Chinese Journal of Sensors and Actuators, 2009, 22(3): 366-370 (in Chinese). 刘准钆, 程咏梅, 潘泉, 等. 多传感器冲突信息的加权融合算法[J]. 传感技术学报, 2009, 22(3): 366-370.
[34] DENG Z, WANG J Y. A novel decision probability transformation method based on belief interval[J]. Knowledge-Based Systems, 2020, 208: 106427.
[35] SMETS P. The application of the matrix calculus to belief functions[J]. International Journal of Approximate Reasoning, 2002, 31(1-2): 1-30.
[36] ZHOU Q, HUANG Y, DENG Y. Belief evolution network: Probability transformation of basic belief assignment and fusion conflict probability[J]. arXiv preprint: 2110.03468, 2021.

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