主观咨询约束下主客观一体化最优赋权方法

doi:10.12305/j.issn.1001-506X.2025.09.21

Abstract

Abstract:

Aiming at the problems of subjective and objective sidedness, high correlation between weight assignment, and lack of subjective consultation constraints in weighting methods such as multiplication synthesis and addition synthesis, a subjective and objective integration weighting optimization method with subjective consultation constraints is proposed. Analyze the subjective constraint type and constrained form connotation, establish a subjective consultation constraints model for regulatory factors, and design the population fitness of regulatory factors based on principal component analysis (PCA), technique for order preference by similarity to ideal solution (TOPSIS), genetic algorithm (GA), and other ideas. Compared with the multiplication synthesis method and the addition synthesis method, the proposed method reduces the redundancy of indicator weights by up to 29.1% and improves accuracy by up to 66.6%. The proposed method has better weighting results and higher scalability.

Key words: subjective consultation constraint, subjective and objective integration, optimal weight, penalty factor

CLC Number:

E 917

Xutao SUN, Yong FU, Weichao WANG. Optimal weighting method for subjective and objective integration with subjective consultation constraints[J]. Systems Engineering and Electronics, 2025, 47(9): 3004-3010.

Figures/Tables 7

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References 31

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指标	指标权重赋值
指标	$ {x_{^1}} $	$ {x_2} $	…	$ {x_L} $
$ {v_{^1}} $	$ {x_{11}} $	$ {x_{12}} $	…	$ {x_{1L}} $
$ {v_2} $	$ {x_{21}} $	$ {x_{22}} $	…	$ {x_{2L}} $
$\vdots $	$\vdots $	$\vdots $		$\vdots $
$ {v_p} $	$ {x_{p1}} $	$ {x_{p2}} $	…	$ {x_{pL}} $

分类条件	分类结果
$ {L_{^1}} > 0 \wedge {L_{^2}} = 0 \wedge {L_{^3}} = 0 $	客观一体化最优权重
$ {L_{^1}} = 0 \wedge {L_{^2}} > 0 \wedge {L_{^3}} = 0 $	主观一体化最优权重
$ {L_{^1}} = 0 \wedge {L_{^2}} = 0 \wedge {L_{^3}} > 0 $	组合赋权一体化最优权重
$ {L_{^1}} > 0 \wedge {L_{^2}} > 0 \wedge {L_{^3}} = 0 $	主客观混合一体化最优权重
$ {L_{^1}} > 0 \wedge {L_{^2}} > 0 \wedge {L_{^3}} > 0 $	主客观与组合赋权一体化最优权重

指标	指标权重赋值						指标约束类型
指标	$ {x_{^1}} $	$ {x_{^2}} $	$\cdots $	$ {x_L} $	$ \alpha {{{\alpha }}^ +_i }/\left\\| {{{\boldsymbol{\alpha }}^ + }} \right\\| $	$ \beta {{{\beta }}^ -_i }/\left\\| {{{\boldsymbol{\beta }}^ - }} \right\\| $	指标约束类型
$ {v_{^1}} $	$ {x_{11}} $	$ {x_{12}} $	$\cdots $	$ {x_{1L}} $	$ \alpha \alpha _1^ + /\left\\| {{\boldsymbol \alpha ^ + }} \right\\| $	$ \beta \beta _1^ - /\left\\| {{\boldsymbol \beta ^ - }} \right\\| $	$ U({v_1}) $
$ {v_2} $	$ {x_{21}} $	$ {x_{21}} $	$\cdots $	$ {x_{2L}} $	$ \alpha \alpha _2^ + /\left\\| {{\boldsymbol \alpha ^ + }} \right\\| $	$\beta \beta _2^ - /\left\\| {{\boldsymbol \beta ^ - }} \right\\| $	$ U({v_2}) $
$\vdots $	$\vdots $	$\vdots $		$\vdots $	$\vdots $	$\vdots $	$\vdots $
$ {v_p} $	$ {x_{p1}} $	$ {x_{p2}} $	$\cdots $	$ {x_{pL}} $	$ \alpha \alpha _p^ + /\left\\| {{\boldsymbol \alpha ^ + }} \right\\| $	$ \beta \beta _p^ - /\left\\| {{\boldsymbol \beta ^ - }} \right\\| $	$ U({v_p}) $

指标	$ {X_{^1}} $	$ {X_2} $	$ {X_3} $	$ {X_4} $	$ {X_5} $	$ {X_6} $	$ {X_7} $	$ {X_8} $	指标约束
电磁信号测试能力A₁	0.206	0.183	0.141	0.215	0.146	0.180	0.215	0.141	$ {W_{{A_1}}} \geqslant 0.18 $
网络安全测试能力A₂	0.152	0.152	0.198	0.120	0.175	0.103	0.198	0.103	$ {W_{{A_2}}} \geqslant 0.12 $
测试发射能力A₃	0.159	0.127	0.226	0.144	0.198	0.180	0.226	0.127	$ {W_{{A_3}}} < 0.25 $
测量控制能力A₄	0.129	0.178	0.113	0.167	0.146	0.180	0.180	0.113	$ {W_{{A_4}}} \geqslant 0.10 $
目标特性测量能力A₅	0.180	0.168	0.164	0.172	0.201	0.208	0.208	0.164	$ {W_{{A_5}}} < 0.20 $
毁伤效应测量能力A₆	0.175	0.193	0.158	0.182	0.134	0.149	0.193	0.134	$ 0.10 < {W_{{A_6}}} < 0.20 $

载荷系数				线性组合系数				综合评分系数
0.537	0.211	−0.707	0.089	2.294	1.573	−8.187	1.183	0.271
0.113	−0.448	−0.113	0.481	0.481	−3.341	−1.314	6.416	−0.196
0.472	−0.137	−0.033	−0.111	2.015	−1.020	−0.386	−1.486	0.323
0.393	−0.481	0.299	−0.580	1.677	−3.587	3.463	−7.734	0.320
−0.064	−0.624	−0.046	0.406	−0.271	−4.652	−0.534	5.415	−0.383
0.504	0.330	0.620	0.466	2.152	2.459	7.184	6.216	0.529
0.241	−0.044	−0.105	−0.152	1.030	−0.331	−1.214	−2.030	0.057
0.079	−0.059	0.008	0.077	0.336	−0.439	0.090	1.022	0.078

Optimal weighting method for subjective and objective integration with subjective consultation constraints

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