基于对数模糊偏好规划的层次化对抗策略评估

doi:10.3969/j.issn.1001-506X.2020.08.20

Abstract

Abstract:

Aiming at the problem of informatization system countermeasures assessment under the conditions of incomplete decision-making information, a assessment method based on logarithmic fuzzy preference programming (LFPP) is proposed. The method combines the analysis of relevant factors in countermeasures assessment with the experience of field experts, builds the hierarchical structure of the countermeasures assessment, and gives the LFPP assessment model and the two-stage integrated approach, which can utilize both the qualitative and quantitative data, produce the unique normalized optimal assessment priority vector for the fuzzy pairwise comparison matrices, and process all the comparison matrices obtained simultaneously and directly in the form of global fuzzy super-matrix to obtain the final priorities. Using the combat aircraft penetration as case study, the result shows that the method can make different optimal countermeasure assessments under different strategy criterias, which can be used to guide the fighter pilot to select the optimal practice actions.

Key words: informatization system, countermeasures assessment, hierarchical, logarithmic fuzzy preference programming (LFPP)

CLC Number:

Yawei GE, Xiqian HOU. Hierarchical countermeasures assessment based on logarithmic fuzzy preference programming[J]. Systems Engineering and Electronics, 2020, 42(8): 1794-1803.

Figures/Tables 10

Table 1

Fig.1

Fig.2

Table 2

Table 3

Table 4

Fuzzy evaluation of the countermeasures choices of the combat aircraft's penetration and confrontation"

C₁₁	MFT	RFT	NoJ	4M+C+F	4M+VRGPO	RGPO	4M+MFT
MFT	(1, 1, 1)	(2/9, 1/4, 2/7)	(2/3, 1, 3/2)	(2/5, 1/2, 2/3)	(1/2, 1, 2)	(1, 2, 3)	(3/2, 2, 5/2)
RFT	(7/2, 4, 9/2)	(1, 1, 1)	(3/2, 2, 5/2)	(3/2, 2, 5/2)	(3/2, 2, 5/2)	(5/2, 3, 7/2)	(2, 3, 4)
NoJ	(2/3, 1, 3/2)	(2/5, 1/2, 2/3)	(1, 1, 1)	(2/3, 1, 3/2)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1, 1, 1)
4M+C+F	(3/2, 2, 5/2)	(2/5, 1/2, 2/3)	(2/3, 1, 3/2)	(1, 1, 1)	(2/3, 1, 3/2)	(3/2, 2, 5/2)	(1/2, 1, 2)
4M+VRGPO	(1/2, 1, 2)	(2/5, 1/2, 2/3)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1, 1, 1)	(1/2, 1, 2)	(1/2, 1, 2)
RGPO	(1/3, 1/2, 1)	(2/7, 1/3, 2/5)	(2/3, 1, 3/2)	(2/5, 1/2, 2/3)	(1/2, 1, 2)	(1, 1, 1)	(3/2, 2, 5/2)
4M+MFT	(2/5, 1/2, 2/3)	(1/4, 1/3, 1/2)	(1/2, 1, 2)	(1/2, 1, 2)	(1/2, 1, 2)	(2/5, 1/2, 2/3)	(1, 1, 1)

C₁₂	MFT	RFT	NoJ	4M+C+F	4M+VRGPO	RGPO	4M+MFT
MFT	(1, 1, 1)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(1, 2, 3)	(2/3, 1, 3/2)	(2/5, 1/2, 2/3)
RFT	(1/2, 1, 2)	(1, 1, 1)	(1, 2, 3)	(1/3, 1/2, 1)	(1/2, 1, 2)	(2/3, 1, 3/2)	(2/7, 1/3, 2/5)
NoJ	(2/3, 1, 3/2)	(1/3, 1/2, 1)	(1, 1, 1)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(1/4, 1/3, 1/2)
4M+C+F	(1/2, 1, 2)	(1, 2, 3)	(2/3, 1, 3/2)	(1, 1, 1)	(1/2, 1, 2)	(2/3, 1, 3/2)	(2/9, 1/4, 2/7)
4M+VRGPO	(1/3, 1/2, 1)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(1, 1, 1)	(1, 2, 3)	(2/5, 1/2, 2/3)
RGPO	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1/3, 1/2, 1)	(1, 1, 1)	(1/2, 1, 2)
4M+MFT	(3/2, 2, 5/2)	(5/2, 3, 7/2)	(2, 3, 4)	(7/2, 4, 9/2)	(3/2, 2, 5/2)	(1/2, 1, 2)	(1, 1, 1)

C₁₃	MFT	RFT	NoJ	4M+C+F	4M+VRGPO	RGPO	4M+MFT
MFT	(1, 1, 1)	(1/2, 1, 2)	(1, 2, 3)	(1/2, 1, 2)	(2/3, 1, 3/2)	(2/5, 1/2, 2/3)	(2/3, 1, 3/2)
RFT	(1/2, 1, 2)	(1, 1, 1)	(2/3, 1, 3/2)	(1/2, 1, 2)	(1, 2, 3)	(2/5, 1/2, 2/3)	(2/3, 1, 3/2)
NoJ	(1/3, 1/2, 1)	(2/3, 1, 3/2)	(1, 1, 1)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(2/7, 1/3, 2/5)	(1/2, 1, 2)
4M+C+F	(1/2, 1, 2)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1, 1, 1)	(1, 1, 1)	(1/4, 1/3, 1/2)	(2/3, 1, 3/2)
4M+VRGPO	(2/3, 1, 3/2)	(1/3, 1/2, 1)	(2/3, 1, 3/2)	(1, 1, 1)	(1, 1, 1)	(2/9, 1/4, 2/7)	(2/3, 1, 3/2)
RGPO	(3/2, 2, 5/2)	(3/2, 2, 5/2)	(5/2, 3, 7/2)	(2, 3, 4)	(7/2, 4, 9/2)	(1, 1, 1)	(3/2, 2, 5/2)
4M+MFT	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(2/5, 1/2, 2/3)	(1, 1, 1)

C₂₁	MFT	RFT	NoJ	4M+C+F	4M+VRGPO	RGPO	4M+MFT
MFT	(1, 1, 1)	(2/5, 1/2, 2/3)	(2/7, 1/3, 2/5)	(2/3, 1, 3/2)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1/2, 1, 2)
RFT	(3/2, 2, 5/2)	(1, 1, 1)	(2/5, 1/2, 2/3)	(3/2, 2, 5/2)	(1, 2, 3)	(1/2, 1, 2)	(2/3, 1, 3/2)
NoJ	(5/2, 3, 7/2)	(3/2, 2, 5/2)	(1, 1, 1)	(3/2, 2, 5/2)	(5/2, 3, 7/2)	(3/2, 2, 5/2)	(2, 3, 4)
4M+C+F	(2/3, 1, 3/2)	(2/5, 1/2, 2/3)	(2/5, 1/2, 2/3)	(1, 1, 1)	(2/3, 1, 3/2)	(1/2, 1, 2)	(2/3, 1, 3/2)
4M+VRGPO	(1/2, 1, 2)	(1/3, 1/2, 1)	(2/7, 1/3, 2/5)	(2/3, 1, 3/2)	(1, 1, 1)	(1, 2, 3)	(1/2, 1, 2)
RGPO	(2/3, 1, 3/2)	(1/2, 1, 2)	(2/5, 1/2, 2/3)	(1/2, 1, 2)	(1/3, 1/2, 1)	(1, 1, 1)	(2/3, 1, 3/2)
4M+MFT	(1/2, 1, 2)	(2/3, 1, 3/2)	(1/4, 1/3, 1/2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1, 1, 1)

C₂₂	MFT	RFT	NoJ	4M+C+F	4M+VRGPO	RGPO	4M+MFT
MFT	(1, 1, 1)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(1/3, 1/2, 1)	(1, 2, 3)	(2/5, 1/2, 2/3)
RFT	(1/2, 1, 2)	(1, 1, 1)	(2/3, 1, 3/2)	(1/3, 1/2, 1)	(1/2, 1, 2)	(1, 2, 3)	(2/7, 1/3, 2/5)
NoJ	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1, 1, 1)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(2/7, 1/3, 2/5)
4M+C+F	(1/2, 1, 2)	(1, 2, 3)	(2/3, 1, 3/2)	(1, 1, 1)	(1/2, 1, 2)	(2/3, 1, 3/2)	(2/9, 1/4, 2/7)
4M+VRGPO	(1, 2, 3)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(1, 1, 1)	(2/3, 1, 3/2)	(2/5, 1/2, 2/3)
RGPO	(1/3, 1/2, 1)	(1/3, 1/2, 1)	(1/2, 1, 2)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1, 1, 1)	(1/4, 1/3, 1/2)
4M+MFT	(3/2, 2, 5/2)	(5/2, 3, 7/2)	(5/2, 3, 7/2)	(7/2, 4, 9/2)	(3/2, 2, 5/2)	(2, 3, 4)	(1, 1, 1)

C₂₃	MFT	RFT	NoJ	4M+C+F	4M+VRGPO	RGPO	4M+MFT
MFT	(1, 1, 1)	(3/2, 2, 5/2)	(7/2, 4, 9/2)	(5/2, 3, 7/2)	(5/2, 3, 7/2)	(3/2, 2, 5/2)	(3/2, 2, 5/2)
RFT	(2/5, 1/2, 2/3)	(1, 1, 1)	(1, 2, 3)	(3/2, 2, 5/2)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1/2, 1, 2)
NoJ	(2/9, 1/4, 2/7)	(1/3, 1/2, 1)	(1, 1, 1)	(2/3, 1, 3/2)	(1/3, 1/2, 1)	(2/3, 1, 3/2)	(1/2, 1, 2)
4M+C+F	(2/7, 1/3, 2/5)	(2/5, 1/2, 2/3)	(2/3, 1, 3/2)	(1, 1, 1)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1/2, 1, 2)
4M+VRGPO	(2/7, 1/3, 2/5)	(1/2, 1, 2)	(1, 2, 3)	(1/2, 1, 2)	(1, 1, 1)	(1/2, 1, 2)	(2/3, 1, 3/2)
RGPO	(2/5, 1/2, 2/3)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(1, 1, 1)	(1/2, 1, 2)
4M+MFT	(2/5, 1/2, 2/3)	(1/2, 1, 2)	(1/2, 1, 2)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(1, 1, 1)

C₃₁	MFT	RFT	NoJ	4M+C+F	4M+VRGPO	RGPO	4M+MFT
MFT	(1, 1, 1)	(7/2, 4, 9/2)	(3/2, 2, 5/2)	(5/2, 3, 7/2)	(3/2, 2, 5/2)	(5/2, 3, 7/2)	(3/2, 2, 5/2)
RFT	(2/9, 1/4, 2/7)	(1, 1, 1)	(1/3, 1/2, 1)	(1/2, 1, 2)	(2/3, 1, 3/2)	(3/2, 2, 5/2)	(1/2, 1, 2)
NoJ	(2/5, 1/2, 2/3)	(1, 2, 3)	(1, 1, 1)	(1/3, 1/2, 1)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1/2, 1, 2)
4M+C+F	(2/7, 1/3, 2/5)	(2/3, 1, 3/2)	(2/5, 1/2, 2/3)	(1, 1, 1)	(2/3, 1, 3/2)	(1/2, 1, 2)	(1/2, 1, 2)
4M+VRGPO	(2/5, 1/2, 2/3)	(1, 2, 3)	(1/2, 1, 2)	(1/2, 1, 2)	(1, 1, 1)	(2/3, 1, 3/2)	(2/3, 1, 3/2)
RGPO	(2/7, 1/3, 2/5)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(1/2, 1, 2)	(1, 1, 1)	(1/2, 1, 2)
4M+MFT	(2/5, 1/2, 2/3)	(1/2, 1, 2)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(1/2, 1, 2)	(1, 1, 1)

C₃₂	MFT	RFT	NoJ	4M+C+F	4M+VRGPO	RGPO	4M+MFT
MFT	(1, 1, 1)	(2/3, 1, 3/2)	(1/2, 1, 2)	(2/3, 1, 3/2)	(2/5, 1/2, 2/3)	(1, 2, 3)	(1/2, 1, 2)
RFT	(2/3, 1, 3/2)	(1, 1, 1)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(2/7, 1/3, 2/5)	(1/2, 1, 2)	(1, 2, 3)
NoJ	(1/2, 1, 2)	(2/3, 1, 3/2)	(1, 1, 1)	(1/2, 1, 2)	(2/5, 1/2, 2/3)	(1/2, 1, 2)	(2/3, 1, 3/2)
4M+C+F	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(1, 1, 1)	(1/4, 1/3, 1/2)	(2/3, 1, 3/2)	(1/2, 1, 2)
4M+VRGPO	(3/2, 2, 5/2)	(5/2, 3, 7/2)	(3/2, 2, 5/2)	(2, 3, 4)	(1, 1, 1)	(5/2, 3, 7/2)	(3/2, 2, 5/2)
RGPO	(1/3, 1/2, 1)	(1/2, 1, 2)	(1/2, 1, 2)	(2/3, 1, 3/2)	(2/7, 1/3, 2/5)	(1, 1, 1)	(1/2, 1, 2)
4M+MFT	(1/2, 1, 2)	(1/3, 1/2, 1)	(2/3, 1, 3/2)	(1/2, 1, 2)	(2/5, 1/2, 2/3)	(1/2, 1, 2)	(1, 1, 1)

C₃₃	MFT	RFT	NoJ	4M+C+F	4M+VRGPO	RGPO	4M+MFT
MFT	(1, 1, 1)	(2/3, 1, 3/2)	(1, 1, 1)	(2/5, 1/2, 2/3)	(1/2, 1, 2)	(3/2, 2, 5/2)	(2/3, 1, 3/2)
RFT	(1/3, 1/2, 1)	(1, 1, 1)	(2/3, 1, 3/2)	(2/5, 1/2, 2/3)	(2/3, 1, 3/2)	(1/2, 1, 2)	(2/3, 1, 3/2)
NoJ	(1, 1, 1)	(2/3, 1, 3/2)	(1, 1, 1)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(2/5, 1/2, 2/3)	(1/2, 1, 2)
4M+C+F	(3/2, 2, 5/2)	(3/2, 2, 5/2)	(2/3, 1, 3/2)	(1, 1, 1)	(2, 3, 4)	(7/2, 4, 9/2)	(3/2, 2, 5/2)
4M+VRGPO	(1/2, 1, 2)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1/4, 1/3, 1/2)	(1, 1, 1)	(1, 2, 3)	(2/3, 1, 3/2)
RGPO	(2/5, 1/2, 2/3)	(1/2, 1, 2)	(3/2, 2, 5/2)	(2/9, 1/4, 2/7)	(1/3, 1/2, 1)	(1, 1, 1)	(1/2, 1, 2)
4M+MFT	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(2/3, 1/2, 2/5)	(2/3, 1, 3/2)	(1/2, 1, 2)	(1, 1, 1)

C₄₁	MFT	RFT	NoJ	4M+C+F	4M+VRGPO	RGPO	4M+MFT
MFT	(1, 1, 1)	(3/2, 2, 5/2)	(5/2, 3, 7/2)	(3/2, 2, 5/2)	(7/2, 4, 9/2)	(5/2, 3, 7/2)	(3/2, 2, 5/2)
RFT	(2/5, 1/2, 2/3)	(1, 1, 1)	(3/2, 2, 5/2)	(2/3, 1, 3/2)	(1, 2, 3)	(1/2, 1, 2)	(1/3, 1/2, 1)
NoJ	(2/7, 1/3, 2/5)	(1/2, 1, 2)	(1, 1, 1)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1/3, 1/2, 1)	(2/5, 1/2, 2/3)
4M+C+F	(2/5, 1/2, 2/3)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1, 1, 1)	(1, 2, 3)	(1/2, 1, 2)	(1/2, 1, 2)
4M+VRGPO	(2/9, 1/4, 2/7)	(1/2, 1, 2)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1, 1, 1)	(1/2, 1, 2)	(2/3, 1, 3/2)
RGPO	(2/7, 1/3, 2/5)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1, 1, 1)	(1/2, 1, 2)
4M+MFT	(2/5, 1/2, 2/3)	(1/2, 1, 2)	(1/2, 1, 2)	(1/2, 1, 2)	(1/2, 1, 2)	(2/3, 1, 3/2)	(1, 1, 1)

C₄₂	MFT	RFT	NoJ	4M+C+F	4M+VRGPO	RGPO	4M+MFT
MFT	(1, 1, 1)	(2/5, 1/2, 2/3)	(2/5, 1/2, 2/3)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(2/3, 1, 3/2)
RFT	(3/2, 2, 5/2)	(1, 1, 1)	(2/5, 1/2, 2/3)	(3/2, 2, 5/2)	(1, 2, 3)	(2/3, 1, 3/2)	(2/3, 1, 3/2)
NoJ	(3/2, 2, 5/2)	(3/2, 2, 5/2)	(1, 1, 1)	(5/2, 3, 7/2)	(5/2, 3, 7/2)	(2, 3, 4)	(3/2, 2, 5/2)
4M+C+F	(2/3, 1, 3/2)	(2/5, 1/2, 2/3)	(2/7, 1/3, 2/5)	(1, 1, 1)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(2/3, 1, 3/2)
4M+VRGPO	(2/3, 1, 3/2)	(1/3, 1/2, 1)	(2/7, 1/3, 2/5)	(2/3, 1, 3/2)	(1, 1, 1)	(1/2, 1, 2)	(2/3, 1, 3/2)
RGPO	(1/2, 1, 2)	(2/3, 1, 3/2)	(1/4, 1/3, 1/2)	(2/3, 1, 3/2)	(1/2, 1, 2)	(1, 1, 1)	(1/2, 1, 2)
4M+MFT	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(2/5, 1/2, 2/3)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(2/3, 1, 3/2)	(1, 1, 1)

Table 4

Table 5

Table 6

Table 7

Fig.3

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步骤	过程或方法	结论或结果
1	结合任务目标,针对问题构建策略网络结构	对抗策略网络结构
2	识别并确定各策略准则以及各准则间的相互关系	对抗策略网络结构中准则与关系模型
3	利用三角模糊判据构建比较矩阵	准则间的模糊成对比较矩阵
4	基于特定方法获取不同层级的规则局部优先级	不同层级的局部优先级
5	利用局部优先级组建未加权的超矩阵¹⁾,并进行归一化处理	归一化的加权超矩阵
6	结合加权超矩阵计算策略准则重要度权重	对抗策略准则的全局优先级序列²⁾

不确定性评估	模糊判据
等或近等	(1, 1, 1)/(1/2, 1, 2)
最有可能x倍更重要于	(x-1, x, x+1)
最有可能x倍不太重要于	(1/(x+1), 1/x, 1/(x-1))
在y和z倍数之间更重要于	(y, (y+z)/2, z)
在y和z倍数之间不太重要于	(1/z, 2/(y+z), 1/y)

敌方探测阵地处于活跃状态(C₁)	Search (C₁₁)	Acquisition (C₁₂)	Non-adaptive Track (C₁₃)
Search (C₁₁)	(1, 1, 1)	(2, 3, 4)	(4, 5, 6)
Acquisition (C₁₂)	(1/4, 1/3, 1/2)	(1, 1, 1)	(1, 2, 3)
Non-adaptive Track (C₁₃)	(1/6, 1/5, 1/4)	(1/3, 1/2, 1)	(1, 1, 1)

探测与跟踪(C₂)	Range Resolution (C₂₁)	Track Maintenance (C₂₂)	Passive Track (C₂₃)
Range Resolution (C₂₁)	(1, 1, 1)	(1/3, 1/2, 1)	(1, 2, 3)
Track Maintenance (C₂₂)	(1, 2, 3)	(1, 1, 1)	(1, 2, 3)
Passive Track (C₂₃)	(1/3, 1/2, 1)	(1/3, 1/2, 1)	(1, 1, 1)

导弹发射与制导(C₃)	Missile Launching (C₃₁)	Mid-Course Guidance (C₃₂)	Terminal Guidance(C₃₃)
Missile Launching (C₃₁)	(1, 1, 1)	(1/9, 1/8, 1/7)	(1/3, 1/2, 1)
Mid-Course Guidance (C₃₂)	(7, 8, 9)	(1, 1, 1)	(2, 3, 4)
Terminal Guidance (C₃₃)	(1, 2, 3)	(1/4, 1/3, 1/2)	(1, 1, 1)

导弹命中(C₄)	Hit (C₄₁)		Miss (C₄₂)
Hit (C₄₁)	(1, 1, 1)		(1/8, 1/7, 1/6)
Miss (C₄₂)	(6, 7, 8)		(1, 1, 1)

战机突防对抗策略评估	敌方探测阵地处于活跃状态(C₁)	探测与跟踪(C₂)	导弹发射与制导(C₃)	导弹命中(C₄)	重要度优先级
敌方探测阵地处于活跃状态(C₁)	(1, 1, 1)	(1/4, 1/3, 1/2)	(1/3, 1/2, 1)	(1, 2, 3)	0.169 4
探测与跟踪(C₂)	(2, 3, 4)	(1, 1, 1)	(1, 2, 3)	(3, 4, 5)	0.448 8
导弹发射与制导(C₃)	(1, 2, 3)	(1/3, 1/2, 1)	(1, 1, 1)	(2, 3, 4)	0.277 2
导弹命中(C₄)	(1/3, 1/2, 1)	(1/5, 1/4, 1/3)	(1/4, 1/3, 1/2)	(1, 1, 1)	0.104 6

突防阶段	对抗策略准则	局部权重值
敌方探测阵地处于活跃状态(C₁, λ=0.834 1)	Search (C₁₁)	0.642 1
	Acquisition (C₁₂)	0.229 2
	Non-adaptive Track (C₁₃)	0.128 7
探测与跟踪(C₂, λ=0.616 7)	Range Resolution (C₂₁)	0.344 1
	Track Maintenance (C₂₂)	0.480 6
	Passive Track (C₂₃)	0.205 3
导弹发射与制导(C₃, λ=0.666 6)	Missile Launching (C₃₁)	0.091 6
	Mid-Course Guidance (C₃₂)	0.697 9
	Terminal Guidance (C₃₃)	0.210 5
导弹命中(C₄, λ=1)	Hit (C₄₁)	0.125 0
导弹命中(C₄, λ=1)	Miss (C₄₂)	0.875 0

Hierarchical countermeasures assessment based on logarithmic fuzzy preference programming

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对抗策略	MFT	RFT	NoJ	4M+C+F	4M+VRGPO	RGPO	4M+MFT	全局权重
C₁₁	0.103 1	0.298 9	0.099 0	0.154 6	0.157 6	0.107 9	0.078 8	0.165 5
C₁₂	0.141 8	0.094 5	0.094 5	0.090 9	0.141 8	0.141 8	0.294 7	0.125 9
C₁₃	0.128 7	0.129 6	0.118 1	0.090 0	0.089 6	0.315 1	0.129 0	0.166 1
C₂₁	0.107 7	0.163 4	0.270 1	0.108 4	0.108 7	0.107 5	0.134 2	0.046 8
C₂₂	0.155 5	0.101 4	0.128 7	0.086 7	0.193 0	0.101 4	0.233 3	0.028 8
C₂₃	0.296 6	0.171 7	0.084 2	0.110 1	0.094 3	0.120 9	0.122 3	0.109 4
C₃₁	0.316 0	0.104 7	0.123 9	0.123 9	0.123 9	0.081 0	0.126 4	0.038 6
C₃₂	0.118 9	0.118 1	0.118 2	0.116 8	0.293 9	0.116 9	0.117 2	0.104 5
C₃₃	0.129 6	0.152 5	0.111 9	0.242 5	0.101 7	0.100 2	0.161 7	0.117 2
C₄₁	0.301 8	0.140 3	0.089 3	0.125 1	0.084 6	0.100 9	0.158 0	0.021 3
C₄₂	0.110 5	0.171 6	0.266 6	0.103 6	0.103 6	0.122 0	0.122 0	0.032 5

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