Damage effectiveness assessment method for anti-ship missiles based on double hierarchy linguistic term sets and evidence theory

doi:10.23919/JSEE.2022.000041

Journal of Systems Engineering and Electronics ›› 2022, Vol. 33 ›› Issue (2): 393-405.doi: 10.23919/JSEE.2022.000041

收稿日期:2020-12-21 接受日期:2022-03-17 出版日期:2022-04-18 发布日期:2022-05-06

Damage effectiveness assessment method for anti-ship missiles based on double hierarchy linguistic term sets and evidence theory

Tianle YAO¹^,*(), Weili WANG¹(), Run MIAO¹(), Jun DONG²(), Xuefei YAN³()

¹ Ordnance Engineering College, Naval University of Engineering, Wuhan 430000, China
² Xi’an Modern Chemistry Research Institute, Xi’an 710065
³ Institute of Systems Engineering, Academy of Military Science, Beijing 100082

Received:2020-12-21 Accepted:2022-03-17 Online:2022-04-18 Published:2022-05-06
Contact: Tianle YAO E-mail:18931970836@163.com;w.l.wang@tom.com;miaorun1769@163.com;94180853@qq.com;jasonyan9023@163.com
About author:YAO Tianle was born in 1994. He received his M.S. degree from Amy Engineering University, China. He is currently a doctoral candidate in Naval University of Engineering. His research interests include weapon system of systems and damage effectiveness assessment.E-mail: 18931970836@163.com
WANG Weili was born in 1962. He is currently a professor in Naval University of Engineering. His research interests include warhead design of missile and damage effectiveness assessment.E-mail: w.l.wang@tom.com
MIAO Run was born in 1989. He received his M.S. and Ph.D. degrees from Naval Aeronautical University, China. His research interests include damage effectiveness assessment and explosion test.E-mail: miaorun1769@163.com
DONG Jun was born in 1982. He received his M.S. degree from Xi’an Modern Chemistry Institute, China. He is currently a doctoral candidate in Naval University of Engineering. His research interests include explosive manufacture.E-mail: 94180853@qq.com
YAN Xuefei was born in 1989. He received his M.S. and Ph.D. degrees from Ordnance Engineering College, China. He is currently a researcher in Academy of Military Science. His research interests include damage effectiveness assessment and warhead power assessment.E-mail: jasonyan9023@163.com

摘要/Abstract

Abstract:

The research on the damage effectiveness assessment of anti-ship missiles involves system science and weapon science, and has essential strategic research significance. With comprehensive analysis of the specific process of the damage assessment process of anti-missile against ships, a synthetic damage effectiveness assessment process is proposed based on the double hierarchy linguistic term set and the evidence theory. In order to improve the accuracy of the expert’s assessment information, double hierarchy linguistic terms are used to describe the assessment opinions of experts. In order to avoid the loss of experts’ original information caused by information fusion rules, the evidence theory is used to fuse the assessment information of various experts on each case. Good stability of the assessment process can be reflected through sensitivity analysis, and the fluctuation of a certain parameter does not have an excessive influence on the assessment results. The assessment process is accurate enough to be reflected through comparative analysis and it has a good advantage in damage effectiveness assessment.

Key words: anti-ship missile, damage effect assessment, linguistic term set, evidence reasoning

. [J]. Journal of Systems Engineering and Electronics, 2022, 33(2): 393-405.

Tianle YAO, Weili WANG, Run MIAO, Jun DONG, Xuefei YAN. Damage effectiveness assessment method for anti-ship missiles based on double hierarchy linguistic term sets and evidence theory[J]. Journal of Systems Engineering and Electronics, 2022, 33(2): 393-405.

图/表 19

Criterion	Expert 1			Expert 2			Expert 3			Expert 4
Criterion	A₁	A₂	A₃	A₁	A₂	A₃	A₁	A₂	A₃	A₁	A₂	A₃
C₁₁	$ \left\{ {{S_{3\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $
C₁₂	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $
C₁₃	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $
C₁₄	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $
C₁₅	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 2\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $
C₁₆	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $
C₁₇	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $
C₁₈	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $
C₁₉	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $
C₂₁	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $
C₂₂	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{ - 1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $
C₂₃	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $
C₂₄	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $
C₂₅	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $
C₂₆	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_2}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_1}} \right\rangle }}} \right\} $
C₂₇	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{1\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{0\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_0}} \right\rangle }}} \right\} $	$ \left\{ {{S_{3\left\langle {{O_{-1}}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_1}} \right\rangle }}} \right\} $	$ \left\{ {{S_{2\left\langle {{O_{-1}}} \right\rangle }}} \right\} $

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Criterion	Expert 1			Expert 2			Expert 3			Expert 4
Criterion	A₁	A₂	A₃	A₁	A₂	A₃	A₁	A₂	A₃	A₁	A₂	A₃
C₁₁	0.2494	0.2533	0.2494	0.2506	0.2497	0.2506	0.2506	0.2437	0.2506	0.2494	0.2533	0.2494
C₁₂	0.2503	0.2515	0.2524	0.2503	0.2515	0.2500	0.2491	0.2455	0.2452	0.2503	0.2515	0.2524
C₁₃	0.2494	0.2509	0.2494	0.2506	0.2485	0.2506	0.2506	0.2497	0.2506	0.2494	0.2509	0.2494
C₁₄	0.2497	0.2521	0.2521	0.2485	0.2521	0.2509	0.2521	0.2437	0.2449	0.2497	0.2521	0.2521
C₁₅	0.2509	0.2512	0.2518	0.2449	0.2537	0.2494	0.2533	0.2439	0.2470	0.2509	0.2512	0.2518
C₁₆	0.2485	0.2470	0.2524	0.2521	0.2530	0.2524	0.2509	0.2530	0.2428	0.2485	0.2470	0.2524
C₁₇	0.2518	0.2500	0.2518	0.2518	0.2500	0.2506	0.2446	0.2500	0.2458	0.2518	0.2500	0.2518
C₁₈	0.2476	0.2497	0.2497	0.2524	0.2473	0.2497	0.2524	0.2533	0.2509	0.2476	0.2497	0.2497
C₁₉	0.2488	0.2509	0.2494	0.2488	0.2485	0.2506	0.2536	0.2497	0.2506	0.2488	0.2509	0.2494
C₂₁	0.2530	0.2515	0.2503	0.2494	0.2503	0.2467	0.2446	0.2467	0.2527	0.2530	0.2515	0.2503
C₂₂	0.2524	0.2515	0.2488	0.2549	0.2503	0.2512	0.2402	0.2467	0.2512	0.2524	0.2515	0.2488
C₂₃	0.2527	0.2491	0.2494	0.2467	0.2515	0.2506	0.2479	0.2503	0.2506	0.2527	0.2491	0.2494
C₂₄	0.2503	0.2485	0.2509	0.2515	0.2509	0.2497	0.2479	0.2521	0.2485	0.2503	0.2485	0.2509
C₂₅	0.2524	0.2464	0.2503	0.2476	0.2536	0.2503	0.2476	0.2536	0.2491	0.2524	0.2464	0.2503
C₂₆	0.2515	0.2497	0.2512	0.2515	0.2509	0.2512	0.2455	0.2497	0.2464	0.2515	0.2497	0.2512
C₂₇	0.2518	0.2497	0.2515	0.2530	0.2485	0.2467	0.2433	0.2521	0.2503	0.2518	0.2497	0.2515

Criterion in the second layer	Criterion in the third layer
Warhead damage capability (0.6)	Missile hit position (0.1)
	Hole size (0.05)
	Number of penetrating cabins (0.05)
	Range of shock wave（0.07）
	Shock wave overpressure (0.07)
	Pressure duration (0.25)
	Number of fragments (0.07)
	Quality of fragment (0.06)
	Initial velocity of fragments (0.1)
Damage resistance of ship (0.4)	Geometry of the ship (0.06)
	Hull bulkhead structure(0.13)
	Hull deck structure (0.1)
	Special structure (0.05)
	Main material of the ship (0.28)
	Ship stiffener (0.22)
	Welding materials for ship (0.16)

Expert	A₁	A₂	A₃
Expert 1	0.1962	0.1613	0.2496
Expert 2	0.2071	0.1817	0.2376
Expert 3	0.2119	0.1107	0.1523
Expert 4	0.1637	0.1931	0.2025

Case	A₁	A₂	A₃
Assessment value	0.1951	0.1590	0.2068

θ/%	w₁	w₂
−30	0.72	0.28
−20	0.68	0.32
−10	0.64	0.36
0	0.60	0.40
10	0.56	0.44
20	0.52	0.48
30	0.48	0.52

Damage effectiveness assessment method for anti-ship missiles based on double hierarchy linguistic term sets and evidence theory

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Criterion	C₁₂	C₁₂	C₁₃	C₁₄	C₁₅	C₁₆	C₁₇	C₁₈	C₁₉
A₁	0.6988	0.5300	0.5054	0.6223	0.5571	0.5421	0.5959	0.5044	0.6292
A₂	0.2055	0.6222	0.3988	0.4149	0.3714	0.4776	0.6810	0.3786	0.4869
A₃	0.6851	0.5761	0.5932	0.6638	0.7428	0.5969	0.4256	0.6231	0.5843