Journal of Systems Engineering and Electronics ›› 2024, Vol. 35 ›› Issue (6): 1469-1481.doi: 10.23919/JSEE.2024.000047
• SYSTEMS ENGINEERING • Previous Articles
Qingyang JIA(), Yajie DOU(
), Nan XIANG(
), Yufeng MA(
), Kewei YANG(
)
Received:
2022-05-24
Online:
2024-12-18
Published:
2025-01-14
Contact:
Yajie DOU
E-mail:cassie_qing@163.com;yajiedou_nudt@163.com;xiangnan1827@163.com;mashuang9707@163.com;kayyang27@nudt.edu.cn
About author:
Supported by:
Qingyang JIA, Yajie DOU, Nan XIANG, Yufeng MA, Kewei YANG. Weapon system selection based on trust network and probabilistic hesitant fuzzy entropy[J]. Journal of Systems Engineering and Electronics, 2024, 35(6): 1469-1481.
Table 1
Symbol description"
Symbol | Description |
A finite set of alternatives | |
A finite set of attributes | |
A finite set of DMs | |
Trust relationship between experts | |
Indirect trust value of the kth trust propagation path between expert | |
Cumulative trust degree from expert | |
Relative node in-degree centrality index of expert | |
Attribute weight vector | |
Expert weight vector | |
Evaluation information of alternative | |
Fuzzy entropy of | |
Hesitant entropy of | |
Total entropy of | |
Grey correlation coefficient of | |
Grey correlation degree of |
Table 2
Initial evaluation results from expert $ {{\boldsymbol{e}}_{\boldsymbol{1}}} $"
Indicator | ||||
{0.2|0.7,0.4|0.3} | {0.4|0.4,0.5|0.6} | {0.3|0.2,0.4|0.5,0.7|0.3} | {0.6|0.2,0.7|0.8} | |
{0.5|0.5,0.7|0.5} | {0.4|0.3,0.5|0.7} | {0.5|0.2,0.8|0.8} | {0.5|0.6,0.7|0.4} | |
{0.6|0.4,0.8|0.4,0.9|0.2} | {0.7|0.8,0.8|0.2} | {0.6|0.4,0.7|0.6} | {0.5|0.5,0.6|0.2,0.9|0.3} | |
{0.5|0.4,0.7|0.6} | {0.2|0.5,0.6|0.2,0.7|0.3} | {0.2|0.5,0.4|0.5} | {0.4|0.5,0.5|0.5} |
Table 3
Initial evaluation results from expert $ {{\boldsymbol{e}}_{\boldsymbol{2}}} $"
Indicator | ||||
{0.4|0.6,0.6|0.4} | {0.6|0.6,0.7|0.4} | {0.4|0.6,0.5|0.4} | {0.3|0.3,0.4|0.7} | |
{0.5|0.3,0.6|0.7} | {0.5|0.4,0.8|0.6} | {0.5|0.6,0.9|0.4} | {0.4|0.2,0.5|0.8} | |
{0.4|0.4,0.8|0.6} | {0.6|0.2,0.7|0.5,0.8|0.3} | {0.3|0.5,0.6|0.5} | {0.4|0.8,0.9|0.2} | |
{0.5|0.5,0.6|0.2,0.7|0.3} | {0.5|0.5,0.7|0.5} | {0.2|0.2,0.6|0.3,0.8|0.5} | {0.4|0.7,0.6|0.3} |
Table 4
Initial evaluation results from expert $ {{\boldsymbol{e}}_{\boldsymbol{3}}} $"
Indicator | ||||
{0.2|0.5,0.4|0.2,0.5|0.3} | {0.5|0.2,0.6|0.4,0.7|0.4} | {0.3|0.2,0.4|0.8} | {0.3|0.4,0.7|0.6} | |
{0.5|0.2,0.7|0.8} | {0.4|0.5,0.7|0.5} | {0.5|0.2,0.7|0.4,0.9|0.4} | {0.4|0.6,0.5|0.1,0.7|0.3} | |
{0.8|0.8,0.9|0.2} | {0.6|0.3,0.8|0.7} | {0.3|0.7,0.5|0.3} | {0.4|0.5,0.6|0.5} | |
{0.6|0.5,0.7|0.5} | {0.5|0.8,0.6|0.2} | {0.6|0.2,0.8|0.8} | {0.4|0.5,0.5|0.2,0.6|0.3} |
Table 5
Initial evaluation results from expert $ {{\boldsymbol{e}}_{\boldsymbol{4}}} $"
Indicator | ||||
{0.2|0.2,0.5|0.8} | {0.4|0.3,0.7|0.7} | {0.3|0.5,0.7|0.5} | {0.4|0.5,0.6|0.5} | |
{0.5|0.1,0.6|0.4,0.7|0.5} | {0.7|0.6,0.8|0.4} | {0.7|0.4,0.9|0.6} | {0.4|0.3,0.7|0.7} | |
{0.4|0.3,0.6|0.3,0.9|0.4} | {0.6|0.5,0.7|0.5} | {0.5|0.2,0.7|0.8} | {0.5|0.5,0.6|0.5} | |
{0.5|0.3,0.6|0.7} | {0.5|0.4,0.6|0.3,0.7|0.3} | {0.4|0.4,0.6|0.1,0.8|0.5} | {0.3|0.4,0.5|0.6} |
Table 6
Total entropy value matrix of the decision matrix"
Expert | Indicator | ||||
Table 8
Probabilistic hesitation fuzzy evaluation matrix for each alternative"
Indicator | ||||
{0.2|0.35,0.4|0.275, 0.5|0.275,0.6|0.1} | {0.4|0.175,0.5|0.2, 0.6|0.25,0.7|0.375} | {0.3|0.225,0.4|0.475,0.5|0.1,0.7|0.2} | {0.3|0.175,0.4|0.3,0.6|0.175,0.7|0.35} | |
{0.5|0.275,0.6|0.275,0.7|0.45} | {0.4|0.2,0.5|0.275, 0.7|0.275,0.8|0.25} | {0.5|0.25,0.7|0.2,0.8|0.2,0.9|0.35} | {0.4|0.275,0.5|0.375,0.7|0.35} | |
{0.4|0.175,0.6|0.175, 0.8|0.45,0.9|0.2} | {0.6|0.25,0.7|0.45,0.8|0.3} | {0.3|0.3,0.5|0.125,0.6|0.225,0.7|0.35} | {0.4|0.325,0.5|0.25,0.6|0.3,0.9|0.125} | |
{0.5|0.3,0.6|0.35,0.7|0.35} | {0.2|0.125,0.5|0.425, 0.6|0.175,0.7|0.275} | {0.2|0.175,0.4|0.225,0.6|0.15,0.8|0.45} | {0.3|0.1,0.4|0.425,0.5|0.325,0.6|0.15} |
Table 9
Calculation results using Liu’s method"
Indicator | ||||||||||||||
Table 11
Differences between the proposed method and Liu’s method"
Comparative item | The proposed method | Liu’s method [ |
Distance measure | Hamming distance | Hamming distance |
Information integration | PHFE entropy | PHFE entropy |
Generation of the attribute weight | Trust network | Not required |
Generation of expert weight | Entropy weight method with expert weight | Entropy weight method |
Ranking reference criteria | GRA | TOPSIS |
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