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The Comprehensive Diagnostic Method Combining Rough Sets and Evidence Theory

Guang Yang
Guang Yang
, 
Shuofeng Yu
Shuofeng Yu
, 
Shan Lu
Shan Lu
 und 
George Smith
George Smith
   | 25. Mai 2021
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Online veröffentlicht: 25. Mai 2021
Seitenbereich: 171 - 180
Eingereicht: 14. Jan. 2021
Akzeptiert: 26. Feb. 2021
DOI: https://doi.org/10.2478/amns.2021.2.00006
Schlüsselwörter
© 2021 Guang Yang et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Structure of diagnostic model integrated with evidence theory and rough set.
Structure of diagnostic model integrated with evidence theory and rough set.

Basic probability assignment about D5.

Verify D1 K m(D1) m(D2) m(D3) m(D4) m(D5) m(Θ)
E1 0 0 0.3167 0 0.3167 0.3167 0.05
E2 0 0.3167 0 0 0.6334 0 0.05
E3 0 0 0 0 0 0.9500 0.05
E1 ⊕E2 DS 0.0531 0.0531 0 0.8326 0.0531 0.0081
Improve DS 0.7020 0.0794 0.1746 0 0.5339 0.1746 0.0375
E1 ⊕E3 DS 0 0.0398 0 0.0398 0.9145 0.0060
Improve DS 0.6017 0 0.1520 0 0.1520 0.6636 0.0324
E2 ⊕E3 DS 0.1624 0 0 0.3248 0.4872 0.0256
Improve DS 0.9025 0.1587 0 0 0.3175 0.4762 0.0476
E1 ⊕E2 ⊕E3 DS 0.0245 0.0245 0 0.3840 0.5634 0.0036
Improve DS 0.9677 0.0688 0.1707 0 0.3191 0.3932 0.0482

Comparison of results of various evidence synthesis methods.

Synthesis formula k m(A) m(B) m(C) m(Θ)
DST 0.99901 0 0 1 0
Yager 0.99901 0 0 0.00099 0.99901
Sun Quan 0.99901 0.3210 0.0030 0.1880 0.4880
Li Bicheng 0.99901 0.6260 0.0067 0.3673 0
This paper 0.99901 0.7321 0.0059 0.2620 0

Table of fault information.

U m(C1) m(C2) m(C3) m(C4) m(C5) D
Original samples 1 0.95 1.40 1.20 5100 0.39 D1
2 0.70 1.74 0.94 3450 0.98 D1
4 0.06 1.73 0.98 3900 0.91 D2
5 0.65 3.31 0.63 1950 0.55 D3
7 0.30 1.31 1.32 4350 0.40 D4
8 0.28 1.23 1.11 4300 0.44 D4
10 0.05 2.47 1.01 3800 0.20 D5
Test samples 3 1.02 1.73 0.57 3500 0.98 D1
6 0.67 3.71 0.77 1900 0.45 D3
9 0.18 0.95 1.14 3600 0.30 D5

Decision table after discretization.

U C1 C2 C3 C4 C5 D
Original samples 1 3 1 3 3 2 D1
2 2 2 2 2 3 D1
4 1 2 2 2 3 D2
5 2 3 1 1 2 D3
7 2 1 3 3 2 D4
8 1 1 2 3 2 D4
10 1 2 2 2 1 D5
Test samples 3 3 2 1 2 3 verify D1
6 2 3 1 1 2 verify D3
9 1 1 2 2 1 verify D5

Basic probability assignment about D1.

Verify D1 K m(D1) m(D2) m(D3) m(D4) m(D5) m(Θ)
E1 0 0.9500 0 0 0 0 0.05
E2 0 0.3167 0.3167 0 0 0.3167 0.05
E3 0 0.4750 0.4750 0 0 0 0.05
E1 ⊕E2 DS 0.9144 0.0397 0 0 0.0397 0.0062
Improve DS 0.6017 0.8269 0.0703 0 0 0.0703 0.0325
E1 ⊕E3 DS 0.9522 0.0433 0 0 0 0.0045
Improve DS 0.4512 0.8899 0.0850 0 0 0 0.0251
E2 ⊕E3 DS 0.4771 0.4771 0 0 0.0397 0.0062
Improve DS 0.6017 0.4282 0.4282 0 0 0.1111 0.0325
E1 ⊕E2 ⊕E3 DS 0.9488 0.0469 0 0 0.0039 0.0006
Improve DS 0.7972 0.7534 0.1498 0 0 0.0569 0.0399
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