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

Abstract

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

CLC Number:

TP391

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.

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References 25

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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

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