基于Pignistic概率转换和奇异值分解的证据冲突度量方法

doi:10.11959/j.issn.1000-436x.2021086

通信学报 ›› 2021, Vol. 42 ›› Issue (4): 150-157.doi: 10.11959/j.issn.1000-436x.2021086

基于Pignistic概率转换和奇异值分解的证据冲突度量方法

郭兴林, 孙振晓, 周昱瑶, 漆莲芝, 张谊

中国工程物理研究院计算机应用研究所，四川绵阳 621900

修回日期:2021-03-24 出版日期:2021-04-25 发布日期:2021-04-01
作者简介:郭兴林（1990- ），男，四川广元人，中国工程物理研究院计算机应用研究所工程师，主要研究方向为可信软件、形式化方法。
孙振晓（1985- ），男，山东泰安人，中国工程物理研究院计算机应用研究所工程师，主要研究方向为可信软件、软件测试。
周昱瑶（1988- ），女，纳西族，云南丽江人，中国工程物理研究院计算机应用研究所工程师，主要研究方向为可信软件、人工智能软件测试。
漆莲芝（1978- ），女，四川成都人，中国工程物理研究院计算机应用研究所高级工程师，主要研究方向为可信软件、人工智能软件测试。
张谊（1974- ），男，四川乐山人，中国工程物理研究院计算机应用研究所高级工程师，主要研究方向为软件测试、软件可靠性、需求建模。
基金资助:
国家国防科技工业局技术基础科研基金资助项目(JSZL2015212B001)

Evidence conflict measurement method based on Pignistic probability transformation and singular value decomposition

Xinglin GUO, Zhenxiao SUN, Yuyao ZHOU, Lianzhi QI, Yi ZHANG

Institute of Computer Application, China Academy of Engineering Physics, Mianyang 621900, China

Revised:2021-03-24 Online:2021-04-25 Published:2021-04-01
Supported by:
The Technical Basic Research Project of State Administration of Science, Technology and Industry for National Defence(JSZL2015212B001)

摘要/Abstract

摘要：

针对常见证据冲突度量方法适应性差、准确性低的问题，提出了一种基于Pignistic概率转换和奇异值分解的证据冲突度量方法。首先通过Pignistic概率转换将证据焦元差异映射到信度差异上，构建证据复合信任函数矩阵。然后采用奇异值分解的方法提取矩阵特征，根据奇异值特性将矩阵特征空间划分为相似子空间和冲突子空间，综合考虑证据矩阵相似特性和冲突特性，将冲突子空间奇异值与相似子空间奇异值之比作为新的冲突度量因子。最后在全冲突场景、变信度场景、变焦元场景、焦元嵌套场景等多种证据冲突场景下将所提方法与常见方法进行了对比分析，结果表明所提方法具有适应性广、准确性高、稳定性好的特点。

关键词: 证据理论, 证据冲突度量, Pignistic概率转换, 奇异值分解

Abstract:

In view of the problem of poor adaptability and low accuracy of common evidence conflict measurement method, an evidence conflict measurement method based on Pignistic probability transformation and singular value decomposition was proposed.First, Pignistic probability transformation was used to map the evidence focal element difference to the belief difference, and the evidence composite belief function matrix was constructed.Then, the matrix features were extracted by singular value decomposition, and the matrix feature space was divided into similar subspace and conflict subspace according to singular value characteristics.Considering the similarity and conflict characteristics of the evidence matrix, and the ratio of the singular value of the conflict subspace to the singular value of the similar subspace was taken as the new conflict measure factor.Finally, the proposed method was compared with common methods in various evidence conflict scenarios, such as full conflict scenario, variable reliability scenario, variable focus element scenario, focal element nested scenario, and the results show that the proposed method has wide adaptability, high accuracy and good stability.

Key words: evidence theory, evidence conflict measurement, Pignistic probability transformation, singular value decom-position

中图分类号:

TP391

郭兴林, 孙振晓, 周昱瑶, 漆莲芝, 张谊. 基于Pignistic概率转换和奇异值分解的证据冲突度量方法[J]. 通信学报, 2021, 42(4): 150-157.

Xinglin GUO, Zhenxiao SUN, Yuyao ZHOU, Lianzhi QI, Yi ZHANG. Evidence conflict measurement method based on Pignistic probability transformation and singular value decomposition[J]. Journal on Communications, 2021, 42(4): 150-157.

图/表 6

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N	K	d_BPA	difBetP	K_d	Cor	diSV	G_SVD
2	1	1	1	1	1	1	1
3	1	1	1	1	1	1	1
4	1	0.833	0.833	0.916 5	0.833	0.833	0.833
5	1	0.7	0.7	0.85	0.7	0.7	0.7
6	1	0.6	0.6	0.8	0.6	0.6	0.6

L	K	d_BPA	difBetP	K_d	Cor	diSV	G_SVD
1	1	1	1	1	1	1	1
2	1	0.707 1	0.5	0.853 6	1	0.707 1	1
3	1	0.571 6	0.33	0.775 8	1	0.571 6	1
4	1	0.5	0.25	0.75	1	0.5	1
5	1	0.447 2	0.2	0.723 6	1	0.447 2	1

m₃	K	d_BPA	difBetP	K_d	Cor	diSV	G_SVD
Φ	0.99	0.9	0.9	0.945 0	0.987 8	0.9	0.987 9
[0 0.1 0.9]	0.999	0.6	0.6	0.799 5	0.658 5	0.6	0.658 6
[0.2 0.1 0.7]	0.999	0.6	0.6	0.799 5	0.580 2	0.574 7	0.606 9
[0.45 0.1 0.45]	0.999	0.6	0.6	0.799 5	0.521 7	0.563 1	0.582 5
[1/3 1/3 1/3]	0.996 7	0.628 1	0.6767	0.812 4	0.569 4	0.569 2	0.599 8
[0.3 0.4 0.3]	0.996	0.646 4	0.7	0.821 2	0.604 5	0.589 0	0.622 4
[0.2 0.6 0.2]	0.994	0.716 3	0.7667	0.855 2	0.729 6	0.679 4	0.721 4
[0 1 0]	0.99	0.9	0.9	0.945 0	0.922 3	0.887 1	0.903 7

N	K	d_BPA	difBetP	K_d	Cor	diSV	G_SVD
1	0.05	0.785 8	0.605 0	0.417 9	0.560 3	0.713 6	0.456 7
2	0.05	0.686 7	0.426 7	0.368 3	0.248 0	0.535 5	0.391 8
3	0.05	0.570 5	0.248 3	0.310 3	0.083 6	0.351 4	0.350 0
4	0.05	0.423 7	0.195 0	0.236 8	0.023 8	0.211 7	0.314 3
5	0.05	0.132 3	0.125 0	0.091 1	0.003 4	0.084 3	0.279 5
6	0.05	0.388 4	0.258 3	0.219 2	0.019 6	0.188 9	0.308 7
7	0.05	0.502 9	0.353 6	0.276 5	0.064 2	0.328 3	0.339 8
8	0.05	0.570 5	0.425 0	0.310	0.106 9	0.410 6	0.357 0
9	0.05	0.618 7	0.480 6	0.334 4	0.152 1	0.480 3	0.371 0
10	0.05	0.655 4	0.525 0	0.352 7	0.196 7	0.540 0	0.382 6
11	0.05	0.684 4	0.561 4	0.367 2	0.239 0	0.592 0	0.392 4
12	0.05	0.708 2	0.591 7	0.379 1	0.278 5	0.638 1	0.400 8
13	0.05	0.728 1	0.617 3	0.389 0	0.314 7	0.679 6	0.408 1
14	0.05	0.745 1	0.639 3	0.397 6	0.347 9	0.717 3	0.414 4
15	0.05	0.759 9	0.658 3	0.405 0	0.378 1	0.751 9	0.420 1
16	0.05	0.773 0	0.675 0	0.411 5	0.405 6	0.783 8	0.425 1
17	0.05	0.784 6	0.689 7	0.417 3	0.430 5	0.813 3	0.429 6
18	0.05	0.795 1	0.702 8	0.422 5	0.453 3	0.840 8	0.433 7
19	0.05	0.804 6	0.714 5	0.427 3	0.473 9	0.866 3	0.437 5
20	0.05	0.813 3	0.725 0	0.431 7	0.492 8	0.889 9	0.440 9

N	K	d_BPA	difBetP	K_d	Cor	diSV	G_SVD
0	1	1	1	1	1	1	1
2	0	0.894 4	0.666 7	0.447 2	0.615 4	0.800 0	0.714 3
4	0	0.774 6	0.428 6	0.387 3	0.310 3	0.600 0	0.555 6
6	0	0.632 5	0.250 0	0.316 2	0.117 6	0.400 0	0.454 5
8	0	0.447 2	0.111 1	0.223 6	0.024 4	0.200 0	0.384 6
10	0	0	0	0	0	0	0

基于Pignistic概率转换和奇异值分解的证据冲突度量方法

Evidence conflict measurement method based on Pignistic probability transformation and singular value decomposition

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N	K	d_BPA	difBetP	K_d	Cor	diSV	G_SVD
2	0	0.707 1	0.500 0	0.353 5	0.179 0	0.581 3	0.261 7
3	0	0.700 3	0.500 0	0.350 2	0.183 1	0.600 8	0.267 5
4	0	0.695 7	0.500 0	0.347 8	0.186 6	0.621 0	0.273 5
5	0	0.692 3	0.500 0	0.346 2	0.189 7	0.640 2	0.279 7
6	0	0.689 7	0.500 0	0.344 8	0.192 3	0.657 5	0.286 0
7	0	0.687 6	0.500 0	0.343 8	0.194 4	0.671 9	0.292 3
8	0	0.685 9	0.500 0	0.342 9	0.195 7	0.682 5	0.298 7
9	0	0.684 4	0.500 0	0.342 2	0.196 0	0.687 5	0.305 1
10	0	0.683 2	0.500 0	0.341 6	0.194 6	0.684 1	0.311 5