基于IVSFS的作战威胁人机协同评估框架

doi:10.12305/j.issn.1001-506X.2025.06.14

Abstract

Abstract:

In response to the uncertainty brought about by different styles of warfare in the era of artificial intelligence, a human-machine collaborative assessment framework of combat threat based on interval-value spherical fuzzy set (IVSFS) is proposed. IVSFS describes decision information in more detail by membership, non-membership, hesitation, and abstention in form of interval numbers. Firstly, a method is proposed to fuse polymorphic temporal interval numbers into IVSFS to process the objective data of the target. Then, the subjective attributes of the target are obtained by experts through the use of a fuzzy terminology set to generate IVSFS. Based on two sets of data, fuzzy entropy is used to obtain indicator weights and establishes an evaluation framework based on grey relation analysis-cumulative prospect theory-technique for order preference by similarity to ideal solution (GRA-CPT-TOPSIS) to assess the threat level of the target through human-machine collaboration. Simulation results show that the proposed method is feasible and effective in comprehensively considering the inherent attributes and dynamic characteristics of the target, making it more suitable for practical warfare scenarios.

Key words: interval-value spherical fuzzy set (IVSFS), human-machine collaboration, polymorphic data fusion, threat assessment

CLC Number:

V271

Chongshuang HU, Jikai WANG, Minghao LI, Yajie DOU, Jiang JIANG. Combat threat human-machine collaborative assessment framework based on IVSFS[J]. Systems Engineering and Electronics, 2025, 47(6): 1855-1866.

Figures/Tables 30

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References 30

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语言术语	表述(缩写)	($ \left[u_{y_{i j}^i}^L(x), u_{y_{i j}^i}^U(x)\right], \left[v_{y_{i j}^i}^L(x), v_{y_{i j}^i}^U(x)\right], \left[\pi_{y_{i j}^i}^L(x), \pi_{y_{i j}^i}^U(x)\right]$)
绝对更重要	Absolutely more importance (AMI)	([0.85, 0.95], [0.10, 0.15], [0.05, 0.15])
非常重要	Very high importance (VHI)	([0.75, 0.85], [0.15, 0.20], [0.15, 0.20])
很重要	High importance (HI)	([0.65, 0.75], [0.20, 0.25], [0.20, 0.25])
稍微更重要	Slightly more importance (SMI)	([0.55, 0.65], [0.25, 0.30], [0.25, 0.30])
相等重要	Equally importance (EI)	([0.50, 0.55], [0.45, 0.55], [0.30, 0.40])
稍微不重要	Slightly low importance (SLI)	([0.25, 0.30], [0.55, 0.65], [0.25, 0.30])
不重要	Low importance (LI)	([0.20, 0.25], [0.65, 0.75], [0.20, 0.25])
非常不重要	Very low importance (VLI)	([0.15, 0.20], [0.75, 0.85], [0.15, 0.20])
绝对不重要	Absolutely low importance (ALI)	([0.10, 0.15], [0.85, 0.95], [0.05, 0.15])

U	T	距离/m	空袭高度/m	速度/(km/h)	航向角/(°)
u₁	t₁	[300, 320]	[700, 800]	[110, 150]	[6, 10]
	t₂	[280, 320]	[820, 850]	[320, 350]	[12, 16]
	t₃	[150, 200]	[1 500, 1 700]	[350, 500]	[3, 6]
	t₄	[520, 550]	[1 200, 1 300]	[280, 350]	[12, 18]
	t₅	[800, 850]	[3 000, 3 500]	[250, 300]	[18, 25]
u₂	t₁	[300, 320]	[720, 820]	[100, 130]	[6, 12]
	t₂	[290, 320]	[800, 850]	[310 ,350]	[12, 16]
	t₃	[100, 160]	[1 500, 1 800]	[340, 500]	[3, 5]
	t₄	[510, 550]	[1 100, 1 300]	[300, 350]	[14, 20]
	t₅	[790, 850]	[3 000, 3 600]	[260, 300]	[16, 25]
u₃	t₁	[310, 320]	[750, 820]	[100, 150]	[8, 10]
	t₂	[290, 300]	[800, 850]	[310, 350]	[12, 16]
	t₃	[110, 180]	[1 600, 1 800]	[380, 500]	[3, 6]
	t₄	[510, 540]	[1 200, 1 400]	[300, 360]	[12, 18]
	t₅	[820, 860]	[2 800, 3 200]	[260, 300]	[16, 24]

T	距离/m	空袭高度/m	速度(km/h)	航向角/(°)
t₁	< [0.28, 0.36], [0.52, 0.58], [0.04, 0.05]>	< [0.55, 0.57], [0.28, 0.31], [0.04, 0.05]>	< [0.21, 0.24], [0.86, 0.87], [0.04, 0.05]>	< [0.15, 0.27], [0.40, 0.56], [0.03, 0.06]>
t₂	< [0.28, 0.36], [0.49, 0.57], [0.04, 0.06]>	< [0.53, 0.55], [0.36, 0.39], [0.05, 0.06]>	< [0.55, 0.57], [0.59, 0.60], [0.04, 0.05]>	< [0.11, 0.17], [0.70, 0.71], [0.04, 0.06]>
t₃	< [0.53, 0.58], [0.05, 0.26], [0.04, 0.06]>	< [0.25, 0.27], [0.66, 0.68], [0.04, 0.07]>	< [0.78, 0.81], [0.52, 0.56], [0.04, 0.05]>	< [0.46, 0.66], [0.17, 0.80], [0.05, 0.06]>
t₄	< [0.16, 0.21], [0.73, 0.75], [0.05, 0.07]>	< [0.34, 0.35], [0.54, 0.58], [0.05, 0.07]>	< [0.56, 0.57], [0.61, 0.64], [0.04, 0.06]>	< [0.09, 0.13], [0.70, 0.78], [0.05, 0.07]>
t₅	< [0.10, 0.14], [0.82, 0.84], [0.05, 0.06]>	< [0.13, 0.13], [0.83, 0.83], [0.04, 0.06]>	< [0.47, 0.49], [0.66, 0.68], [0.04, 0.05]>	< [0.07, 0.11], [0.78, 0.80], [0.06, 0.06]>

E	T	类型	侦察	干扰	打击	防御
e₁	t₁	SMI	SMI	HI	SLI	SMI
	t₂	SLI	VHI	VLI	ALI	SML
	t₃	VHI	VLI	SLI	AMI	EI
	t₄	EI	SMI	EI	SMI	SLI
	t₅	HI	LI	LI	HI	VHI
e₂	t₁	HI	SMI	SMI	HI	EI
	t₂	SMI	AMI	EI	VLI	LI
	t₃	VHI	VLI	VLI	VHI	AMI
	t₄	SMI	EI	HI	EI	SMI
	t₅	VHI	EI	HI	EI	EI
e₃	t₁	SMI	EI	HI	EI	EI
	t₂	EI	VHI	HI	VLI	LI
	t₃	VHI	LI	VLI	VHI	VHI
	t₄	SMI	SMI	HI	EI	SLI
	t₅	HI	VHI	VHI	SMI	EI

e	t₁	t₂	t₃	t₄	t₅	距离类型
e₁	0.06	0.12	0.07	0.07	0.15	DGWMD_i^k
e₂	0.05	0.06	0.03	0.05	0.07
e₃	0.03	0.07	0.02	0.04	0.08
e₁	0.07	0.14	0.07	0.09	0.17	DGBD_i^k
e₂	0.03	0.09	0.04	0.03	0.14
e₃	0.08	0.10	0.05	0.06	0.08
e₁	0.05	0.06	0.04	0.03	0.08	DGWD_i^k
e₂	0.08	0.11	0.06	0.09	0.11
e₃	0.04	0.11	0.05	0.06	0.17

Combat threat human-machine collaborative assessment framework based on IVSFS

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指标	e₁	e₂	e₃
贴近度指数CI^(k)	0.64	0.75	0.77
修复后的专家权重	0.29	0.35	0.36

类别	类型	侦察	干扰	打击	防御
模糊熵	0.66	0.61	0.47	0.69	0.60
权重	0.17	0.20	0.27	0.16	0.20

Ω⁺	类型	侦察	干扰	打击	防御
t₁	0.13	0.24	0.00	0.27	0.25
t₂	0.28	0.00	0.14	0.67	0.33
t₃	0.00	0.62	0.45	0.00	0.00
t₄	0.20	0.24	0.02	0.29	0.32
t₅	0.05	0.22	0.02	0.21	0.17

Ω^－	类型	侦察	干扰	打击	防御
t₁	0.14	0.38	0.45	0.41	0.09
t₂	0.00	0.62	0.31	0.00	0.00
t₃	0.28	0.00	0.00	0.67	0.33
t₄	0.08	0.38	0.43	0.40	0.03
t₅	0.22	0.40	0.44	0.47	0.16

Y⁺	类型	侦察	干扰	打击	防御
t₁	0.72	0.58	1.00	0.56	0.57
t₂	0.55	1.00	0.71	0.33	0.51
t₃	1.00	0.35	0.43	1.00	1.00
t₄	0.63	0.58	0.95	0.54	0.51
t₅	0.87	0.60	0.95	0.62	0.66

Y^－	类型	侦察	干扰	打击	防御
t₁	0.70	0.47	0.43	0.45	0.79
t₂	1.00	0.35	0.52	1.00	1.00
t₃	0.55	1.00	1.00	0.33	0.51
t₄	0.81	0.47	0.44	0.46	0.91
t₅	0.60	0.46	0.43	0.42	0.68

Θ⁺	类型	侦察	干扰	打击	防御
t₁	0.43	0.48	0.72	0.48	0.33
t₂	0.28	0.81	0.51	0.17	0.25
t₃	0.64	0.18	0.21	0.84	0.66
t₄	0.36	0.48	0.69	0.47	0.27
t₅	0.54	0.50	0.70	0.55	0.41

Θ^－	类型	侦察	干扰	打击	防御
t₁	0.42	0.36	0.21	0.36	0.52
t₂	0.64	0.18	0.33	0.84	0.66
t₃	0.28	0.81	0.72	0.17	0.25
t₄	0.50	0.36	0.23	0.37	0.62
t₅	0.33	0.34	0.22	0.31	0.43

H⁺	类型	侦察	干扰	打击	防御
t₁	0.62	0.68	0.81	0.68	0.52
t₂	0.41	0.84	0.70	0.20	0.38
t₃	0.75	0.23	0.32	0.85	0.77
t₄	0.54	0.68	0.80	0.66	0.43
t₅	0.71	0.69	0.80	0.72	0.61

H^－	类型	侦察	干扰	打击	防御
t₁	-1.38	-1.26	-0.72	-1.26	-1.58
t₂	-1.69	-0.52	-1.20	-1.92	-1.74
t₃	-0.92	-1.90	-1.82	-0.46	-0.86
t₄	-1.53	-1.26	-0.79	-1.28	-1.70
t₅	-1.13	-1.23	-0.79	-1.12	-1.42

T	类型	侦察	干扰	打击	防御
t₁	< [0.59, 0.69], [0.23, 0.28], [0.05, 0.08]>	< [0.53, 0.62], [0.31, 0.37], [0.07, 0.11]>	< [0.62, 0.72], [0.22, 0.27], [0.05, 0.07]>	< [0.52, 0.6], [0.36, 0.44], [0.06, 0.10]>	< [0.52, 0.58], [0.38, 0.46], [0.08, 0.14]>
t₂	< [0.47, 0.54], [0.39, 0.47], [0.07, 0.12]>	< [0.79, 0.9], [0.13, 0.18], [0.01, 0.03]>	< [0.51, 0.59], [0.39, 0.47], [0.05, 0.10]>	< [0.14, 0.19], [0.78, 0.88], [0.02, 0.04]>	< [0.42, 0.50], [0.46, 0.54], [0.04, 0.07]>
t₃	< [0.75, 0.85], [0.15, 0.20], [0.02, 0.04]>	< [0.17, 0.22], [0.71, 0.81], [0.03, 0.05]>	< [0.19, 0.23], [0.68, 0.78], [0.03, 0.06]>	< [0.79, 0.89], [0.13, 0.18], [0.02, 0.03]>	< [0.75, 0.86], [0.18, 0.24], [0.03, 0.05]>
t₄	< [0.54, 0.62], [0.30, 0.36], [0.07, 0.11]>	< [0.53, 0.62], [0.31, 0.37], [0.07, 0.11]>	< [0.61, 0.71], [0.25, 0.32], [0.05, 0.08]>	< [0.52, 0.58], [0.38, 0.46], [0.08, 0.14]>	< [0.39, 0.47], [0.42, 0.50], [0.06, 0.09]>
t₅	< [0.69, 0.79], [0.18, 0.23], [0.03, 0.05]>	< [0.58, 0.67], [0.34, 0.42], [0.05, 0.08]>	< [0.63, 0.73], [0.26, 0.32], [0.03, 0.06]>	< [0.57, 0.66], [0.29, 0.35], [0.06, 0.10]>	< [0.60, 0.69], [0.32, 0.41], [0.06, 0.11]>

指标	p_ij
t₁	-0.27
t₂	-0.57
t₃	-0.35
t₄	-0.38
t₅	-0.10

指标	r_ij
t₁	-0.64
t₂	-0.77
t₃	-0.49
t₄	-0.78
t₅	-0.77

方法	专家群体E	无人集群U
TOPSIS	t₅>t₁>t₄>t₃>t₂	t₃>t₂>t₁>t₄>t₅
GRA	t₅>t₁>t₄>t₃>t₂	t₃>t₂>t₁>t₄>t₅
GRA-TOPSIS	t₅>t₁>t₄>t₃>t₂	t₃>t₂>t₁>t₄>t₅
GRA-CPT-TOPSIS	t₅>t₁>t₄>t₃>t₂	t₃>t₂>t₁>t₄>t₅

正负权重	类型	侦察	干扰	打击	防御
v_ij⁺	0.19	0.20	0.23	0.18	0.20
v_ij^－	0.18	0.20	0.24	0.17	0.20

类别	距离	空袭高度	速度	航向角
模糊熵	0.62	0.63	0.54	0.69
权重	0.25	0.24	0.30	0.20

方法	综合威胁度R	d₁	d₂	d₃	d₄
文献[6]	t₃(1.00)>t₁(0.98)>t₂(0.88)>t₅(0.86)>t₄(0.78)	0.02	0.10	0.02	0.09
文献[7]	t₃(0.64)>t₁(0.59)>t₂(0.53)>t₅(0.52)>t₄(0.50)	0.08	0.10	0.02	0.04
文献[8]	t₃(0.87)>t₁(0.73)>t₂(0.64)>t₅(0.61)>t₄(0.58)	0.16	0.12	0.05	0.05
文献[9]	t₃(0.43)>t₁(0.37)>t₂(0.30)>t₅(0.28)>t₄(0.27)	0.14	0.19	0.07	0.04
本文算法	t₃(－0.49)>t₁(－0.64)>t₂(－0.77)>t₅(－0.77)>t₄(－0.78)	0.31	0.20	0.01	0.01

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