Journal of Systems Engineering and Electronics ›› 2022, Vol. 33 ›› Issue (5): 1161-1172.doi: 10.23919/JSEE.2022.000112
• SYSTEMS ENGINEERING • Previous Articles Next Articles
Ziwei ZHANG1,2(
), Qisheng GUO1,*(), Zhiming DONG1(), Hongxiang LIU3(), Ang GAO1(), Pengcheng QI1()
Received:2021-11-15
Accepted:2022-06-13
Online:2022-10-27
Published:2022-10-27
Contact:
Qisheng GUO
E-mail:41872293@qq.com;Qisheng.Guo@163.com;dong_zhiming@163.com;13811816672@139.com;15689783388@163.com;13573129023@139.com
About author:Supported by:Ziwei ZHANG, Qisheng GUO, Zhiming DONG, Hongxiang LIU, Ang GAO, Pengcheng QI. Operational effectiveness evaluation based on the reduced conjunctive belief rule base[J]. Journal of Systems Engineering and Electronics, 2022, 33(5): 1161-1172.
Fig 1
Classification and relationship of operational effectiveness"
Fig 2
Basic structure of the operational effectiveness evaluation index system"
Table 1
Complete conjunctive BRB"
| Serial number | Rule premise | Rule conclusion |
| 1 | | |
| 2 | | |
| 3 | | |
| 4 | | |
| 5 | | |
| 6 | | |
| 7 | | |
| 8 | | |
| 9 | | |
| 10 | | |
| 11 | | |
| 12 | | |
| 13 | | |
| 14 | | |
| 15 | | |
| 16 | | |
| 17 | | |
| 18 | | |
| 19 | | |
| 20 | | |
| 21 | | |
| 22 | | |
| 23 | | |
| 24 | | |
| 25 | | |
| 26 | | |
| 27 | | |
Table 2
Standard disjunctive BRB"
| Serial number | Rule premise | Rule conclusion |
| 1 | | |
| 2 | | |
| 3 | | |
Fig 3
Comprehensive design and orthogonal design comparison"
Table 3
Orthogonal table ${{\boldsymbol{L}}_{\boldsymbol{9}}}({{\boldsymbol{3}}^{\boldsymbol{4}}})$ "
| Line number | Factor | |||
| a | b | c | d | |
| 1 | 0 | 0 | 0+0=0 | 0×2+0=0 |
| 2 | 0 | 1 | 0+1=1 | 0×2+1=1 |
| 3 | 0 | 2 | 0+2=2 | 0×2+2=2 |
| 4 | 1 | 0 | 1+0=1 | 1×2+0=2 |
| 5 | 1 | 1 | 1+1=2 | 1×2+1=0 |
| 6 | 1 | 2 | 1+2=0 | 1×2+2=1 |
| 7 | 2 | 0 | 2+0=2 | 2×2+0=1 |
| 8 | 2 | 1 | 2+1=0 | 2×2+1=2 |
| 9 | 2 | 2 | 2+2=1 | 2×2+2=0 |
| Listing | a | b | a+b | a×2+b |
Table 4
Reduced conjunctive BRB"
| Serial number | Rule premise | Rule conclusion |
| 1 | | |
| 5 | | |
| 9 | | |
| 11 | | |
| 15 | | |
| 16 | | |
| 21 | | |
| 22 | | |
| 26 | | |
Fig 4
Operational mission effectiveness evaluation index system"
Table 5
Complete conjunctive BRB of the “Operational loss”"
| Serial number | Rule item: (c31= | Rule conclusion: c3= ( |
| 1 | c31=0, c32=0, c33=0 | c3= (1,0,0) |
| 2 | c31=0, c32=0, c33=0.5 | c3= (0.9,0.1,0) |
| 3 | c31=0, c32=0, c33=1 | c3= (0.8,0.2,0) |
| 4 | c31=0, c32=0.5, c33=0 | c3= (0.2,0.8,0) |
| 5 | c31=0, c32=0.5, c33=0.5 | c3= (0.2,0.8,0) |
| 6 | c31=0, c32=0.5, c33=1 | c3= (0.2,0.8,0) |
| 7 | c31=0, c32=1, c33=0 | c3= (0,0.4,0.6) |
| 8 | c31=0, c32=1, c33=0.5 | c3= (0,0.4,0.6) |
| 9 | c31=0, c32=1, c33=1 | c3= (0,0.4,0.6) |
| 10 | c31=0.5, c32=0, c33=0 | c3= (0,0.3,0.7) |
| 11 | c31=0.5, c32=0, c33=0.5 | c3= (0,0.3,0.7) |
| 12 | c31=0.5, c32=0, c33=1 | c3= (0,0.3,0.7) |
| 13 | c31=0.5, c32=0.5, c33=0 | c3= (0,0.2,0.8) |
| 14 | c31=0.5, c32=0.5, c33=0.5 | c3= (0,0.2,0.8) |
| 15 | c31=0.5, c32=0.5, c33=1 | c3= (0,0.2,0.8) |
| 16 | c31=0.5, c32=1, c33=0 | c3= (0,0.1,0.9) |
| 17 | c31=0.5, c32=1, c33=0.5 | c3= (0,0.1,0.9) |
| 18 | c31=0.5, c32=1, c33=1 | c3= (0,0.1,0.9) |
| 19 | c31=1, c32=0, c33=0 | c3= (0,0,1) |
| 20 | c31=1, c32=0, c33=0.5 | c3= (0,0,1) |
| 21 | c31=1, c32=0, c33=1 | c3= (0,0,1) |
| 22 | c31=1, c32=0.5, c33=0 | c3= (0,0,1) |
| 23 | c31=1, c32=0.5, c33=0.5 | c3= (0,0,1) |
| 24 | c31=1, c32=0.5, c33=1 | c3= (0,0,1) |
| 25 | c31=1, c32=1, c33=0 | c3= (0,0,1) |
| 26 | c31=1, c32=1, c33=0.5 | c3= (0,0,1) |
| 27 | c31=1, c32=1, c33=1 | c3= (0,0,1) |
Table 6
Reasoning based on the complete conjunctive BRB"
| Serial number | Evaluation input: (c31,c32,c33) | Evaluation output: (light, medium, heavy) | Effectiveness: E |
| 1 | (0.1,0.6,0.4) | (0.099 9,0.624 9,0.275 2) | 0.412 3 |
| 2 | (0.6,0.5,0.9) | (0.000 0,0.130 5,0.869 5) | 0.065 3 |
| 3 | (0.2,0.1,0.3) | (0.447 0,0.276 0,0.277 0) | 0.585 0 |
| 4 | (0.9,0.8,0.9) | (0.000 0,0.015 8,0.984 2) | 0.007 9 |
| 5 | (0.5,0.4,0.5) | (0.000 0,0.195 5,0.804 5) | 0.097 8 |
| 6 | (0.8,0.9,0.7) | (0.000 0,0.032 7,0.967 3) | 0.016 4 |
| 7 | (0.4,0.3,0.7) | (0.070 7,0.269 4,0.659 8) | 0.205 4 |
| 8 | (0.3,0.2,0.6) | (0.201 1,0.325 2,0.473 7) | 0.363 7 |
| 9 | (0.7,0.7,0.8) | (0.000 0,0.064 6,0.935 4) | 0.032 3 |
Table 7
Reduced conjunctive BRB of the “Operational loss”"
| Serial number | Rule item: (c31= | Rule conclusion: c3= ( |
| 1 | c31=0, c32=0, c33=0 | c3= (1,0,0) |
| 2 | c31=0, c32=0.5, c33=0.5 | c3= (0.2,0.8,0) |
| 3 | c31=0, c32=1, c33=1 | c3= (0,0.4,0.6) |
| 4 | c31=0.5, c32=0, c33=0.5 | c3= (0,0.3,0.7) |
| 5 | c31=0.5, c32=0.5, c33=1 | c3= (0,0.2,0.8) |
| 6 | c31=0.5, c32=1, c33=0 | c3= (0,0.1,0.9) |
| 7 | c31=1, c32=0, c33=1 | c3= (0,0,1) |
| 8 | c31=1, c32=0.5, c33=0 | c3= (0,0,1) |
| 9 | c31=1, c32=1, c33=0.5 | c3= (0,0,1) |
Table 8
Standard disjunctive BRB of the “Operational loss”"
| Serial number | Rule item: (c31= | Rule conclusion: c3= ( |
| 1 | c31=0, c32=0, c33=0 | c3= (0.403 6, 0.3128, 0.2836) |
| 2 | c31=0.5, c32=0.5, c33=0.5 | c3= (0.005 4, 0.1785, 0.8161) |
| 3 | c31=1, c32=1, c33=1 | c3= (0.000 0, 0.0264, 0.9736) |
Table 9
Reasoning based on the disjunctive BRB"
| Serial number | Evaluation input: (c31,c32,c33) | Evaluation output: (light, medium, heavy) | Effectiveness: E′ |
| 1 | (0.1,0.6,0.4) | (0.123 5,0.199 5,0.677 0) | 0.223 3 |
| 2 | (0.6,0.5,0.9) | (0.003 4,0.118 6,0.878 0) | 0.062 8 |
| 3 | (0.2,0.1,0.3) | (0.229 3,0.255 7,0.515 0) | 0.357 2 |
| 4 | (0.9,0.8,0.9) | (0.001 1,0.052 7,0.946 2) | 0.027 5 |
| 5 | (0.5,0.4,0.5) | (0.014 4,0.182 1,0.803 5) | 0.105 4 |
| 6 | (0.8,0.9,0.7) | (0.001 4,0.060 3,0.938 3) | 0.031 6 |
| 7 | (0.4,0.3,0.7) | (0.044 8,0.152 5,0.802 7) | 0.121 1 |
| 8 | (0.3,0.2,0.6) | (0.078 1,0.167 9,0.753 9) | 0.162 1 |
| 9 | (0.7,0.7,0.8) | (0.002 2,0.082 4,0.915 4) | 0.043 4 |
Fig 5
Comparison of evaluation results under the two evaluation methods"
Table 10
Discrimination of evaluation results under the two methods"
| Serial number | Evaluation input: (c31,c32,c33) | Reasoning evaluation of the complete conjunctive BRB | Reasoning evaluation of the reduced conjunctive BRB | |||
| Effectiveness: E | Difference ratio: D | Effectiveness: E′ | Difference ratio: D′ | |||
| 3 | (0.2,0.1,0.3) | 0.585 0 | 0.295 2 | 0.357 2 | 0.374 9 | |
| 1 | (0.1,0.6,0.4) | 0.412 3 | 0.117 9 | 0.223 3 | 0.274 0 | |
| 8 | (0.3,0.2,0.6) | 0.363 7 | 0.435 2 | 0.162 1 | 0.253 1 | |
| 7 | (0.4,0.3,0.7) | 0.205 4 | 0.524 1 | 0.121 1 | 0.129 2 | |
| 5 | (0.5,0.4,0.5) | 0.097 8 | 0.332 3 | 0.105 4 | 0.404 7 | |
| 2 | (0.6,0.5,0.9) | 0.065 3 | 0.504 9 | 0.062 8 | 0.308 8 | |
| 9 | (0.7,0.7,0.8) | 0.032 3 | 0.493 9 | 0.043 4 | 0.272 4 | |
| 6 | (0.8,0.9,0.7) | 0.016 4 | 0.516 8 | 0.031 6 | 0.129 7 | |
| 4 | (0.9,0.8,0.9) | 0.007 9 | ? | 0.027 5 | ? | |
| Discrimination | 0.402 5 | ? | 0.268 3 | ? | ||
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