Improved Base Belief Function-Based Conflict Data Fusion Approach Considering Belief Entropy in the Evidence Theory
<p>The flowchart of the proposed method.</p> "> Figure 2
<p>Comparison of fusion results using different methods in Example 3.</p> "> Figure 3
<p>Comparison of fusion results using different methods in Example 4.</p> "> Figure 4
<p>Comparison of fusion results using different methods in Example 5.</p> "> Figure 5
<p>The calculation process of this experiment.</p> ">
Abstract
:1. Introduction
2. Preliminaries
2.1. Dempster–Shafer Evidence Theory
2.2. Belief Entropy
2.3. Improved Base Belief Function
3. Proposed Method
3.1. Method
- Step 1:
- Step 2:
- For the ith evidence, the information volume is calculated through the Deng entropy [39]. is defined as follows:
- Step 3:
- For each evidence, the weight is defined as follows:
- Step 4:
- The weights are obtained through step 3 to modify the BPAs before fusing data. After evidence modification using the base belief function and information volume-based uncertainty, the final evidence for data fusion can be calculated as follows:
- Step 5:
- The final evidence obtained by step 4 can be fused through the Dempster combination rule in Equation (4) to get the final result. If there are n bodies of evidence, then the modified evidence will be fused with times.
- Step 6:
- Decision making based on the data fusion result.
3.2. Examples and Discussion
4. Application of Proposed Method
4.1. Experiment 1
4.2. Experiment 2
5. Open Issues
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Method | m(a) | m(b) | m(c) | m() | m() | m() | m() |
---|---|---|---|---|---|---|---|
Dempster’s rule | 0.9 | 0 | 0 | 0.1 | 0 | 0 | 0 |
Improved base belief function [45] | 0.3587 | 0.1405 | 0.3278 | 0.0656 | 0.0468 | 0.0468 | 0.0193 |
Proposed method | 0.3669 | 0.1278 | 0.3479 | 0.0541 | 0.0426 | 0.0426 | 0.0180 |
Method | m(a) | m(b) | m(c) | m() | m() | m() | m() |
---|---|---|---|---|---|---|---|
Dempster’s rule | 0.4865 | 0.0270 | 0.4865 | 0 | 0 | 0 | 0 |
Improved base belief function [45] | 0.3365 | 0.1653 | 0.3365 | 0.0485 | 0.0485 | 0.0485 | 0.0162 |
Proposed method | 0.3446 | 0.1571 | 0.3446 | 0.0461 | 0.0461 | 0.0461 | 0.0154 |
Method | m(a) | m(b) | m(c) | m() | m() | m() | m() |
---|---|---|---|---|---|---|---|
Dempster’s rule | 0.3448 | 0.0345 | 0.6207 | 0 | 0 | 0 | 0 |
Improved base belief function [45] | 0.3502 | 0.1418 | 0.3480 | 0.0469 | 0.0469 | 0.0469 | 0.0193 |
Proposed method | 0.3734 | 0.1302 | 0.3481 | 0.0433 | 0.0433 | 0.0433 | 0.0184 |
Attribute | m(a) | m(b) | m(c) | m() | m() | m() | m() |
---|---|---|---|---|---|---|---|
SL | 0.3337 | 0.3165 | 0.2816 | 0.0307 | 0.0052 | 0.0272 | 0.0052 |
SW | 0.3164 | 0.2501 | 0.2732 | 0.0304 | 0.0481 | 0.0515 | 0.0304 |
PL | 0.6699 | 0.3258 | 0 | 0 | 0 | 0.0043 | 0 |
PW | 0.6996 | 0.2778 | 0 | 0 | 0 | 0.0226 | 0 |
Attribute | m(a) | m(b) | m(c) | m() | m() | m() | m() |
---|---|---|---|---|---|---|---|
SL | 0.3337 | 0.3165 | 0.2816 | 0.0307 | 0.0052 | 0.0272 | 0.0052 |
SW | 0.3164 | 0.2501 | 0.2732 | 0.0304 | 0.0481 | 0.0515 | 0.0304 |
PL | 0.4064 | 0.2343 | 0.0714 | 0.0714 | 0.0714 | 0.0736 | 0.0714 |
PW | 0.4212 | 0.2103 | 0.0714 | 0.0714 | 0.0714 | 0.0827 | 0.0714 |
Method | m(a) | m(b) | m(c) | m() |
---|---|---|---|---|
Improved base belief function [45] | 0.6232 | 0.2671 | 0.1083 | 0 |
Proposed method | 0.6798 | 0.2385 | 0.0869 | 0 |
Sample 1 | = 0.6486 | = 0.7477 | = 0.8650 | = 0 |
= 0 | = 0 | = 0 | = 0.9000 | |
= 0 | = 0 | = 0.0821 | = 0 | |
= 0 | = 0 | = 0 | = 0.1 | |
= 0.3514 | = 0.2523 | = 0.0529 | = 0 | |
Sample 2 | = 0.6486 | = 0.7477 | = 0.2712 | = 0 |
= 0 | = 0 | = 0 | = 0.9000 | |
= 0 | = 0 | = 0 | = 0 | |
= 0 | = 0 | = 0 | = 0.1 | |
= 0.3514 | = 0.2523 | = 0.7288 | = 0 | |
Sample 3 | = 0.6486 | = 0.7547 | = 0.1356 | = 0 |
= 0 | = 0 | = 0 | = 0.9000 | |
= 0 | = 0 | = 0 | = 0 | |
= 0 | = 0 | = 0 | = 0.1 | |
= 0.3514 | = 0.2453 | = 0.8644 | = 0 | |
Sample 4 | = 0.6857 | = 0 | = 0.8650 | = 0 |
= 0 | = 0 | = 0 | = 0.9000 | |
= 0 | = 0 | = 0.0821 | = 0 | |
= 0 | = 0 | = 0 | = 0.1 | |
= 0.3143 | = 1 | = 0.0529 | = 0 | |
Sample 5 | = 0 | = 0.3738 | = 0.7560 | = 0 |
= 0 | = 0 | = 0 | = 0.9000 | |
= 0 | = 0 | = 0.1484 | = 0 | |
= 0 | = 0 | = 0 | = 0.1 | |
= 1 | = 0.6262 | = 0.0956 | = 0 | |
Sample 6 | = 0.8649 | = 0.7477 | = 0.6780 | = 0 |
= 0 | = 0 | = 0 | = 0.9000 | |
= 0 | = 0 | = 0 | = 0 | |
= 0 | = 0 | = 0 | = 0.1 | |
= 0.1351 | = 0.2523 | = 0.3220 | = 0 | |
Sample 7 | = 0.6857 | = 0.7547 | = 0.7560 | = 0 |
= 0 | = 0 | = 0 | = 0.9000 | |
= 0 | = 0 | = 0.1484 | = 0 | |
= 0 | = 0 | = 0 | = 0.1 | |
= 0.3143 | = 0.2453 | = 0.0956 | = 0 | |
Sample 8 | = 0.8649 | = 0.7547 | = 0.4068 | = 0 |
= 0 | = 0 | = 0 | = 0.9000 | |
= 0 | = 0 | = 0 | = 0 | |
= 0 | = 0 | = 0 | = 0.1 | |
= 0.1351 | = 0.2453 | = 0.5932 | = 0 | |
Sample 9 | = 0.9143 | = 0.7547 | = 0.5253 | = 0 |
= 0 | = 0 | = 0 | = 0.9000 | |
= 0 | = 0 | = 0.2887 | = 0 | |
= 0 | = 0 | = 0 | = 0.1 | |
= 0.0857 | = 0.2453 | = 00.1860 | = 0 | |
Sample 10 | = 0.8649 | = 0.7547 | = 0.8650 | = 0 |
= 0 | = 0 | = 0 | = 0.9000 | |
= 0 | = 0 | = 0.0821 | = 0 | |
= 0 | = 0 | = 0 | = 0.1 | |
= 0.1351 | = 0.2453 | = 0.0529 | = 0 |
Sample 1 | Improved base belief function | 0.6158 | 0.2641 | 0.1014 | 0.0258 | 0.1014 | 0.0134 | 0.0017 |
Proposed method | 0.6639 | 0.2259 | 0.0862 | 0.0300 | 0.0099 | 0.0120 | 0.0022 | |
Sample 2 | Improved base belief function | 0.4781 | 0.3376 | 0.1346 | 0.0299 | 0.0193 | 0.0255 | 0.0051 |
Proposed method | 0.5303 | 0.2690 | 0.1229 | 0.0394 | 0.0218 | 0.0253 | 0.0092 | |
Sample 3 | Improved base belief function | 0.4604 | 0.3549 | 0.1401 | 0.0310 | 0.0207 | 0.0273 | 0.0056 |
Proposed method | 0.4992 | 0.2853 | 0.1316 | 0.0422 | 0.0251 | 0.0290 | 0.0118 | |
Sample 4 | Improved base belief function | 0.4811 | 0.3378 | 0.1295 | 0.0281 | 0.0167 | 0.0217 | 0.0035 |
Proposed method | 0.4893 | 0.2999 | 0.1283 | 0.0459 | 0.0240 | 0.0279 | 0.0110 | |
Sample 5 | Improved base belief function | 0.3875 | 0.4038 | 0.1404 | 0.0329 | 0.0214 | 0.0281 | 0.0055 |
Proposed method | 0.4216 | 0.3237 | 0.1410 | 0.0557 | 0.0301 | 0.0345 | 0.0168 | |
Sample 6 | Improved base belief function | 0.6168 | 0.2589 | 0.1070 | 0.0260 | 0.0116 | 0.0151 | 0.0022 |
Proposed method | 0.6639 | 0.2209 | 0.0897 | 0.0278 | 0.0107 | 0.0129 | 0.0025 | |
Sample 7 | Improved base belief function | 0.6057 | 0.2868 | 0.1001 | 0.0278 | 0.0104 | 0.0135 | 0.0018 |
Proposed method | 0.6623 | 0.2305 | 0.0836 | 0.0326 | 0.0096 | 0.0115 | 0.0021 | |
Sample 8 | Improved base belief function | 0.5658 | 0.2973 | 0.1192 | 0.0281 | 0.0144 | 0.0187 | 0.0030 |
Proposed method | 0.6021 | 0.2469 | 0.1061 | 0.0336 | 0.0157 | 0.0185 | 0.0050 | |
Sample 9 | Improved base belief function | 0.6304 | 0.3157 | 0.0913 | 0.0315 | 0.0087 | 0.0112 | 0.0013 |
Proposed method | 0.6614 | 0.2443 | 0.0744 | 0.0377 | 0.0077 | 0.0093 | 0.0014 | |
Sample 10 | Improved base belief function | 0.6680 | 0.2355 | 0.0902 | 0.0251 | 0.0080 | 0.0103 | 0.0011 |
Proposed method | 0.7023 | 0.2098 | 0.0748 | 0.0254 | 0.0071 | 0.0087 | 0.0011 |
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Ni, S.; Lei, Y.; Tang, Y. Improved Base Belief Function-Based Conflict Data Fusion Approach Considering Belief Entropy in the Evidence Theory. Entropy 2020, 22, 801. https://doi.org/10.3390/e22080801
Ni S, Lei Y, Tang Y. Improved Base Belief Function-Based Conflict Data Fusion Approach Considering Belief Entropy in the Evidence Theory. Entropy. 2020; 22(8):801. https://doi.org/10.3390/e22080801
Chicago/Turabian StyleNi, Shuang, Yan Lei, and Yongchuan Tang. 2020. "Improved Base Belief Function-Based Conflict Data Fusion Approach Considering Belief Entropy in the Evidence Theory" Entropy 22, no. 8: 801. https://doi.org/10.3390/e22080801