Journal of Computer Applications ›› 2024, Vol. 44 ›› Issue (7): 2144-2150.DOI: 10.11772/j.issn.1001-9081.2023070982
• Advanced computing • Previous Articles Next Articles
Received:
2023-07-20
Revised:
2023-09-15
Accepted:
2023-09-20
Online:
2023-10-26
Published:
2024-07-10
Contact:
Bin SUO
About author:
GAO Peigen, born in 1996, M. S. candidate. His research interests include experimental design and modeling, reliability optimized design.Supported by:
通讯作者:
锁斌
作者简介:
高培根(1996—),男,四川眉山人,硕士研究生,主要研究方向:实验设计与建模、可靠性优化设计;基金资助:
CLC Number:
Peigen GAO, Bin SUO. Experimental design and staged PSO-Kriging modeling based on weighted hesitant fuzzy set[J]. Journal of Computer Applications, 2024, 44(7): 2144-2150.
高培根, 锁斌. 基于加权犹豫模糊集的实验设计与分阶段PSO-Kriging建模[J]. 《计算机应用》唯一官方网站, 2024, 44(7): 2144-2150.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2023070982
ek | ||
---|---|---|
[-10,-0.125],[-0.125,10] | [-10,-0.4],[-0.4,10] | |
e1 | [-10,-1],[ | [-10,-0.7],[-0.7,10] |
e2 | [-10,-0.5],[-0.5,10] | [-10,-0.2],[-0.2,10] |
e3 | [-10,1],[ | [-10,0.3],[0.3,10] |
e4 | [-10,0],[0,10] | [-10,-1],[ |
Tab. 1 Experimental interval division results
ek | ||
---|---|---|
[-10,-0.125],[-0.125,10] | [-10,-0.4],[-0.4,10] | |
e1 | [-10,-1],[ | [-10,-0.7],[-0.7,10] |
e2 | [-10,-0.5],[-0.5,10] | [-10,-0.2],[-0.2,10] |
e3 | [-10,1],[ | [-10,0.3],[0.3,10] |
e4 | [-10,0],[0,10] | [-10,-1],[ |
ek | Ai | C1 | C2 | C3 |
---|---|---|---|---|
e1 | A1 | 0.6 | 0.5 | 0.5 |
A2 | 0.1 | 0.1 | 0.1 | |
A3 | 0.9 | 0.8 | 0.7 | |
A4 | 0.8 | 0.7 | 0.9 | |
e2 | A1 | 0.7 | 0.6 | 0.5 |
A2 | 0.2 | 0.1 | 0.1 | |
A3 | 0.8 | 0.8 | 0.8 | |
A4 | 0.7 | 0.8 | 0.7 | |
e3 | A1 | 0.7 | 0.7 | 0.7 |
A2 | 0.1 | 0.2 | 0.1 | |
A3 | 0.9 | 0.9 | 0.8 | |
A4 | 0.8 | 0.7 | 0.8 | |
e4 | A1 | 0.6 | 0.5 | 0.7 |
A2 | 0.2 | 0.1 | 0.1 | |
A3 | 0.8 | 0.9 | 0.7 | |
A4 | 0.6 | 0.7 | 0.8 |
Tab. 2 Evaluation matrix of experts
ek | Ai | C1 | C2 | C3 |
---|---|---|---|---|
e1 | A1 | 0.6 | 0.5 | 0.5 |
A2 | 0.1 | 0.1 | 0.1 | |
A3 | 0.9 | 0.8 | 0.7 | |
A4 | 0.8 | 0.7 | 0.9 | |
e2 | A1 | 0.7 | 0.6 | 0.5 |
A2 | 0.2 | 0.1 | 0.1 | |
A3 | 0.8 | 0.8 | 0.8 | |
A4 | 0.7 | 0.8 | 0.7 | |
e3 | A1 | 0.7 | 0.7 | 0.7 |
A2 | 0.1 | 0.2 | 0.1 | |
A3 | 0.9 | 0.9 | 0.8 | |
A4 | 0.8 | 0.7 | 0.8 | |
e4 | A1 | 0.6 | 0.5 | 0.7 |
A2 | 0.2 | 0.1 | 0.1 | |
A3 | 0.8 | 0.9 | 0.7 | |
A4 | 0.6 | 0.7 | 0.8 |
波动性指标 | A1 | A2 | A3 | A4 |
---|---|---|---|---|
C1 | {〈0.6,0.499 1〉,〈0.7,0.500 9〉} | {〈0.1,0.487 9〉,〈0.2,0.512 1〉} | {〈0.8,0.512 1〉,〈0.9,0.487 9〉} | {〈0.6,0.249 5〉,〈0.7,0.262 5〉,〈0.8,0.487 9〉} |
C2 | {〈0.5,0.499 1〉,〈0.6,0.262 5〉,〈0.7,0.238 4〉} | {〈0.1,0.761 6〉,〈0.2,0.238 4〉,} | {〈0.8,0.512 1〉,〈0.9,0.487 9〉} | {〈0.7,0.737 5〉,〈0.8,0.262 5〉} |
C3 | {〈0.5,0.512 1〉,〈0.7,0.487 9〉} | {〈0.1,1〉} | {〈0.7,0.499 1〉,〈0.8,0.500 9〉} | {〈0.7,0.262 5〉,〈0.8,0.487 9〉,〈0.9,0.249 5〉} |
Tab. 3 Region A1 - A4 are based on evaluation results of weighted hesitant fuzzy elements
波动性指标 | A1 | A2 | A3 | A4 |
---|---|---|---|---|
C1 | {〈0.6,0.499 1〉,〈0.7,0.500 9〉} | {〈0.1,0.487 9〉,〈0.2,0.512 1〉} | {〈0.8,0.512 1〉,〈0.9,0.487 9〉} | {〈0.6,0.249 5〉,〈0.7,0.262 5〉,〈0.8,0.487 9〉} |
C2 | {〈0.5,0.499 1〉,〈0.6,0.262 5〉,〈0.7,0.238 4〉} | {〈0.1,0.761 6〉,〈0.2,0.238 4〉,} | {〈0.8,0.512 1〉,〈0.9,0.487 9〉} | {〈0.7,0.737 5〉,〈0.8,0.262 5〉} |
C3 | {〈0.5,0.512 1〉,〈0.7,0.487 9〉} | {〈0.1,1〉} | {〈0.7,0.499 1〉,〈0.8,0.500 9〉} | {〈0.7,0.262 5〉,〈0.8,0.487 9〉,〈0.9,0.249 5〉} |
p | A1 | A2 | A3 | A4 |
---|---|---|---|---|
30 | 6 | 4 | 11 | 9 |
35 | 8 | 5 | 12 | 10 |
40 | 9 | 6 | 14 | 11 |
45 | 9 | 7 | 16 | 13 |
50 | 11 | 7 | 18 | 14 |
Tab. 4 Subdesign region sample size
p | A1 | A2 | A3 | A4 |
---|---|---|---|---|
30 | 6 | 4 | 11 | 9 |
35 | 8 | 5 | 12 | 10 |
40 | 9 | 6 | 14 | 11 |
45 | 9 | 7 | 16 | 13 |
50 | 11 | 7 | 18 | 14 |
p | ||
---|---|---|
30 | 1.200 6 | [0.443 2,0.307 1] |
35 | 1.310 4 | [0.421 8,0.256 1] |
40 | 1.458 0 | [0.375 8,0.259 6] |
45 | 1.500 2 | [0.367 2,0.249 0] |
50 | 1.482 5 | [0.355 0,0.250 7] |
Tab. 5 Kriging model parameter values
p | ||
---|---|---|
30 | 1.200 6 | [0.443 2,0.307 1] |
35 | 1.310 4 | [0.421 8,0.256 1] |
40 | 1.458 0 | [0.375 8,0.259 6] |
45 | 1.500 2 | [0.367 2,0.249 0] |
50 | 1.482 5 | [0.355 0,0.250 7] |
p | 拟合优度 | 均方根误差 | ||||
---|---|---|---|---|---|---|
本文方法 | HSS | LHD | 本文方法 | HSS | LHD | |
30 | 0.965 3 | 0.962 7 | 0.890 6 | 0.424 8 | 0.440 6 | 0.754 2 |
35 | 0.985 7 | 0.972 8 | 0.904 2 | 0.273 0 | 0.375 2 | 0.703 4 |
40 | 0.991 2 | 0.978 8 | 0.972 4 | 0.213 4 | 0.331 7 | 0.378 7 |
45 | 0.996 6 | 0.990 1 | 0.963 9 | 0.133 7 | 0.227 5 | 0.433 0 |
50 | 0.997 5 | 0.991 0 | 0.978 4 | 0.113 1 | 0.215 0 | 0.356 3 |
Tab. 6 Test results of goodness-of-fit and root mean square error
p | 拟合优度 | 均方根误差 | ||||
---|---|---|---|---|---|---|
本文方法 | HSS | LHD | 本文方法 | HSS | LHD | |
30 | 0.965 3 | 0.962 7 | 0.890 6 | 0.424 8 | 0.440 6 | 0.754 2 |
35 | 0.985 7 | 0.972 8 | 0.904 2 | 0.273 0 | 0.375 2 | 0.703 4 |
40 | 0.991 2 | 0.978 8 | 0.972 4 | 0.213 4 | 0.331 7 | 0.378 7 |
45 | 0.996 6 | 0.990 1 | 0.963 9 | 0.133 7 | 0.227 5 | 0.433 0 |
50 | 0.997 5 | 0.991 0 | 0.978 4 | 0.113 1 | 0.215 0 | 0.356 3 |
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