Optimization of Crucial Targets for Air Defense Based on Combined Weighting-TOPSIS Model

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

Abstract

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

CLC Number:

TJ706.1

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.

Figures/Tables 16

Fig. 1

Table 1

Correlation of evaluation factors for defended targets

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		$b 11$	$b 12$	$b 13$	$b 21$	$b 22$	$b 23$	$b 24$	$b 31$	$b 32$	$b 33$	$b 34$	$b 41$	$b 42$	$b 43$
$B 1$	$b 11$	√	√	√	√	√	×	√	√	×	×	√	√	√	√
	$b 12$	√	√	√	√	√	×	√	√	×	×	√	√	×	√
	$b 13$	√	√	√	√	√	×	√	√	×	×	√	√	×	√
$B 2$	$b 21$	√	√	√	√	√	√	√	√	×	√	√	√	√	√
	$b 22$	√	√	√	√	√	√	√	√	√	√	√	√	√	√
	$b 23$	×	×	×	√	√	√	√	√	×	√	√	√	√	√
	$b 24$	√	√	√	√	√	√	√	√	√	√	√	√	√	√
$B 3$	$b 31$	√	√	√	√	√	√	√	√	√	√	√	√	√	√
	$b 32$	×	×	×	×	√	×	√	√	√	×	√	×	√	√
	$b 33$	×	×	×	√	√	√	√	√	×	√	√	×	×	×
	$b 34$	√	√	√	√	√	√	√	√	√	√	√	×	×	×
$B 4$	$b 41$	√	√	√	√	√	√	√	√	×	×	×	√	√	√
	$b 42$	√	×	×	√	√	√	√	√	√	×	×	√	√	√
	$b 43$	√	√	√	√	√	√	√	√	√	×	×	√	√	√

Table 1

Fig. 2

Table 2

Target attribute data

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

Table 2

Table 3

Comparison matrix of B1 factor group to b21

$B 1$	$b 11$	$b 12$	$b 13$	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

Table 3

Table 4

Comparison matrix of B2 factor group to b21

$B 2$	$b 21$	$b 22$	$b 23$	$b 24$	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

Table 4

Table 5

Comparison matrix of B3 factor group to b21

$B 3$	$b 31$	$b 33$	$b 34$	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

Table 5

Table 6

Comparison matrix of B4 factor group to b21

$B 4$	$b 41$	$b 42$	$b 43$	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

Table 6

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Table 7

Total ranked weights of hierarchy

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

Table 7

Table 8

Objective weights of evaluation factors

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

Table 8

Table 9

Calculation process of the ideal solution for defended targets

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

Table 9

Fig. 7

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