基于组合赋权-TOPSIS模型的防空重点保卫目标优选

doi:10.16182/j.issn1004731x.joss.23-0946

摘要/Abstract

摘要：

为优化区域防空作战重点保卫目标的选择，提高选择重点保卫目标的准确性，从目标价值、保卫迫切程度、目标易损性和目标恢复性四方面构建防空保卫目标重要程度因素模型。采用网络层次分析法（analytic network process，ANP）和熵权法组合赋权的方式对TOPSIS法进行优化，克服多因素评价过程中指挥员倾向性的主观意见和过于依赖客观数据的问题，提升因素赋权的合理性和准确性；利用超级决策软件Super Decisions对ANP法权重进行计算，加快数据处理速度。实例分析结果表明：模型符合指挥员作战倾向及任务实际，验证了模型的可行性和准确性，对加强防空作战辅助决策提供可靠的参考及依据。

关键词: 区域防空, 重点保卫目标, 目标优选, 组合赋权-TOPSIS法, 超级决策

Abstract:

To optimize the selection of crucial defended targets in regional air defense operations and improve the selection accuracy, this paper constructs a factor model considering the importance of air defense targets from the perspectives of target value, defense urgency, target vulnerability, and target recovery. Under the optimization of the TOPSIS method through a combination of the ANP and entropy weight methods, tendentious opinions of commanders and the excessive reliance on objective data can be overcome to ensure the factor weighting is more reasonable and accurate; Super Decisions is used to calculate the weights of the ANP method, accelerating data processing. Case analysis shows that this model, conforming to the commander's operational tendency and task reality, is feasible and accurate in practice. It can provide a reliable reference for strengthening the auxiliary decision-making of air defense operations.

Key words: regional air defense, crucial defended target, target selection, combined weighting-TOPSIS method, super decisions

中图分类号:

TJ706.1

张鹏,冯柯 . 基于组合赋权-TOPSIS模型的防空重点保卫目标优选[J]. 系统仿真学报, 2024, 36(11): 2644-2653.

Zhang Peng,Feng Ke . Optimization of Crucial Targets for Air Defense Based on Combined Weighting-TOPSIS Model[J]. Journal of System Simulation, 2024, 36(11): 2644-2653.

图/表 16

图1

表1

保卫目标评价因素相互关联性

关联性		目标价值 $B 1$			保卫迫切程度 $B 2$				目标易损性 $B 3$				目标恢复性 $B 4$
关联性		$b 11$	$b 12$	$b 13$	$b 21$	$b 22$	$b 23$	$b 24$	$b 31$	$b 32$	$b 33$	$b 34$	$b 41$	$b 42$	$b 43$
$B 1$	$b 11$	√	√	√	√	√	×	√	√	×	×	√	√	√	√
	$b 12$	√	√	√	√	√	×	√	√	×	×	√	√	×	√
	$b 13$	√	√	√	√	√	×	√	√	×	×	√	√	×	√
$B 2$	$b 21$	√	√	√	√	√	√	√	√	×	√	√	√	√	√
	$b 22$	√	√	√	√	√	√	√	√	√	√	√	√	√	√
	$b 23$	×	×	×	√	√	√	√	√	×	√	√	√	√	√
	$b 24$	√	√	√	√	√	√	√	√	√	√	√	√	√	√
$B 3$	$b 31$	√	√	√	√	√	√	√	√	√	√	√	√	√	√
	$b 32$	×	×	×	×	√	×	√	√	√	×	√	×	√	√
	$b 33$	×	×	×	√	√	√	√	√	×	√	√	×	×	×
	$b 34$	√	√	√	√	√	√	√	√	√	√	√	×	×	×
$B 4$	$b 41$	√	√	√	√	√	√	√	√	×	×	×	√	√	√
	$b 42$	√	×	×	√	√	√	√	√	√	×	×	√	√	√
	$b 43$	√	√	√	√	√	√	√	√	√	×	×	√	√	√

表1

图2

表2

目标属性数据

目标	保卫目标属性
目标	$b 11$	$b 12$	$b 13$	$b 21$	$b 22$	$b 23$	$b 24$	$b 31$	$b 32$	$b 33$	$b 34$	$b 41$	$b 42$	$b 43$
$a 11$	1.6	1.2	3.2	2.9	2.5	1.5	4.0	2.0	5.0	2.5	4.8	2.3	1.9	1.5
$a 12$	5.0	3.2	1.4	4.6	4.9	4.9	4.6	4.6	2.5	3.0	1.9	4.8	1.3	3.4
$a 13$	3.5	1.5	0.8	4.0	2.6	2.8	2.1	3.6	1.2	4.3	2.6	4.0	1.2	3.0
$a 14$	0.3	4.5	2.4	1.3	3.8	3.3	3.5	0.5	4.6	3.7	3.8	1.2	2.0	3.8

表2

表3

B1因素组对b21的比较矩阵

$B 1$	$b 11$	$b 12$	$b 13$	权重值
$b 11$	1	3	5	0.648 0
$b 12$	1/3	1	2	0.229 9
$b 13$	1/5	1/2	1	0.122 2

表3

表4

B2因素组对b21的比较矩阵

$B 2$	$b 21$	$b 22$	$b 23$	$b 24$	权重值
$b 21$	1	5	7	2	0.519 5
$b 22$	1/5	1	2	1/3	0.108 5
$b 23$	1/7	1/2	1	1/6	0.060 1
$b 24$	1/2	3	6	1	0.312 0

表4

表5

B3因素组对b21的比较矩阵

$B 3$	$b 31$	$b 33$	$b 34$	权重值
$b 31$	1	6	2	0.612 7
$b 33$	1/6	1	1/2	0.118 0
$b 34$	1/2	2	1	0.269 3

表5

表6

B4因素组对b21的比较矩阵

$B 4$	$b 41$	$b 42$	$b 43$	权重值
$b 41$	1	1/3	1/2	0.163 8
$b 42$	3	1	2	0.539 0
$b 43$	2	1/2	1	0.297 3

表6

图3

图4

图5

图6

表7

层次总排序权重

目标因素		$B 1$	$B 2$	$B 3$	$B 4$	$w j$
$B 1$	$b 11$	0.365	0	0	0	0.120
	$b 12$	0.341	0	0	0	0.112
	$b 13$	0.294	0	0	0	0.097
$B 2$	$b 21$	0	0.425	0	0	0.128
	$b 22$	0	0.136	0	0	0.041
	$b 23$	0	0.065	0	0	0.020
	$b 24$	0	0.374	0	0	0.113
$B 3$	$b 31$	0	0	0.283	0	0.047
	$b 32$	0	0	0.246	0	0.041
	$b 33$	0	0	0.098	0	0.016
	$b 34$	0	0	0.373	0	0.062
$B 4$	$b 41$	0	0	0	0.227	0.046
	$b 42$	0	0	0	0.324	0.066
	$b 43$	0	0	0	0.449	0.091

表7

表8

评价因素客观权重

因素	$b 11$	$b 12$	$b 13$	$b 21$	$b 22$	$b 23$	$b 24$	$b 31$	$b 32$	$b 33$	$b 34$	$b 41$	$b 42$	$b 43$
$X$	1.600	1.200	3.200	2.900	2.500	1.500	4.000	2.000	5.000	2.500	4.800	2.300	1.900	1.500
	5.000	3.200	1.400	4.600	4.900	4.900	4.600	4.600	2.500	3.000	1.900	4.800	1.300	3.400
	3.500	1.500	0.800	4.000	2.600	2.800	2.100	3.600	1.200	4.300	2.600	4.000	1.200	3.000
	0.300	4.500	2.400	1.300	3.800	3.300	3.500	0.500	4.600	3.700	3.800	1.200	2.000	3.800
$p i j$	0.141	0	0.522	0.211	0	0	0.328	0.172	0.447	0	0.527	0.147	0.437	0
	0.511	0.357	0.130	0.434	0.631	0.523	0.431	0.471	0.153	0.143	0	0.480	0.063	0.333
	0.348	0.054	0	0.355	0.026	0.200	0	0.356	0	0.514	0.127	0.373	0	0.263
	0	0.589	0.348	0	0.342	0.277	0.241	0	0.400	0.343	0.345	0	0.500	0.403
$l n p i j$	-1.957	-9.739	-0.651	-1.558	-9.670	-9.859	-1.116	-1.758	-0.805	-9.876	-0.640	-1.919	-0.827	-10.118
	-0.672	-1.030	-2.037	-0.834	-0.460	-0.648	-0.842	-0.752	-1.878	-1.946	-9.851	-0.734	-2.772	-1.099
	-1.056	-2.926	-9.861	-1.035	-3.635	-1.609	-10.052	-1.032	-10.016	-0.665	-2.061	-0.985	-9.904	-1.335
	-9.882	-0.529	-1.056	-10.045	-1.073	-1.284	-1.421	-9.963	-0.916	-1.070	-1.063	-9.945	-0.693	-0.908
$e j$	0.712	0.604	0.702	0.763	0.544	0.734	0.773	0.740	0.732	0.712	0.698	0.723	0.636	0.782
$w j'$	0.069	0.096	0.072	0.057	0.110	0.064	0.055	0.063	0.065	0.069	0.073	0.067	0.088	0.053

表8

表9

保卫目标理想解的计算过程

因素	$b 11$	$b 12$	$b 13$	$b 21$	$b 22$	$b 23$	$b 24$	$b 31$	$b 32$	$b 33$	$b 34$	$b 41$	$b 42$	$b 43$
$Z i j$	0.050	0	0.664	0.123	0	0	0.305	0.079	0.521	0	0.672	0.055	0.430	0
	0.649	0.267	0.041	0.525	0.772	0.701	0.529	0.586	0.061	0.051	0	0.589	0.009	0.324
	0.301	0.006	0	0.351	0.001	0.103	0	0.335	0	0.657	0.039	0.356	0	0.202
	0	0.727	0.295	0	0.227	0.197	0.166	0	0.417	0.292	0.289	0	0.561	0.474
$C$	0.006	0	0.066	0.013	0	0	0.027	0.003	0.020	0	0.044	0.002	0.035	0
	0.077	0.041	0.004	0.055	0.049	0.013	0.046	0.025	0.002	0.001	0	0.026	0.001	0.022
	0.036	0.001	0	0.037	0	0.002	0	0.014	0	0.011	0.003	0.016	0	0.014
	0	0.111	0.029	0	0.014	0.004	0.015	0	0.016	0.005	0.019	0	0.046	0.032
$X +$	0.077	0.111	0.066	0.055	0.049	0.013	0.046	0.025	0.020	0.011	0.044	0.026	0.046	0.032
$X -$	0	0	0	0	0	0	0	0	0	0	0	0	0	0

表9

图7

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