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摘要:
针对粗糙集(RS)理论在处理评估问题时,无法处理决策属性缺失的信息系统的问题,提出一种基于信息熵(IE)和粗糙集的空中目标威胁评估模型。该模型通过信息熵方法计算各属性权重,选取最大权重的属性替代决策属性,构建完备的粗糙集决策信息系统,并根据属性重要性方法进行离散化处理,基于决策辨识矩阵实现属性约简和权重计算,对空中目标的威胁程度进行量化评估。模型拓宽了粗糙集理论在评估中的适用范围,减少对先验信息的需求与人为主观因素的影响。仿真结果表明,该方法可以实现对空中目标的有效评估。
Abstract:Aimed at the problem that rough set (RS) theory cannot deal with information system without decision when evaluation issues are processed, an air target threat evaluation model based on information entropy (IE) and RS is put forward. The model adopts IE method to calculate the attribute weights, chooses the attribute with maximal weight to replace the decision attribute, and establishes a complete RS decision information system. Furthermore, the data is discretized via attribute importance method. Then attribute reduction and weight calculation have been realized with decision identification matrix, and the threat degree of air targets could be quantitatively evaluated. The model provides rough set theory a broader application field, reduces the requirement for prior information as well as the influence of subjective factors. The simulation results show that the proposed method can realize an effective evaluation for air target.
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Key words:
- air target /
- surface air defense /
- rough set (RS) /
- information entropy (IE) /
- threat evaluation
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表 1 目标威胁数据库数据
Table 1. Data of target threat database
目标 a1 a2/(m·s-1) a3/(°) a4 a5 a6/m t1 大型目标 500 130 强 高 360 t2 大型目标 550 90 中 中 160 t3 小型目标 600 50 中 高 160 t4 小型目标 750 150 中 超低 400 t5 直升机 88 140 无 超低 320 t6 直升机 90 180 弱 低 170 表 2 初始信息表
Table 2. Initial information
目标 a1 a2/(m·s-1) a3/(°) a4 a5 a6/m t1 2 500 130 4 4 360 t2 2 550 90 3 3 160 t3 3 600 50 3 4 160 t4 3 750 150 3 1 400 t5 1 88 140 1 1 320 t6 1 90 180 2 2 170 表 3 归一化决策矩阵
Table 3. Decision matrix after normalization
目标 a1 a2 a3 a4 a5 a6 t1 0.1977 0.2505 0.2505 0.2738 0.2897 0.2399 t2 0.1755 0.0430 0.0430 0.0017 0.0017 0.0012 t3 0.1782 0.0416 0.0416 0.0352 0.0054 0.0024 t4 0.2672 0.1731 0.1731 0.3355 0.5326 0.4845 t5 0.0943 0.3586 0.3586 0.3123 0.1704 0.2720 t6 0.0871 0.1332 0.1332 0.0415 0.0002 0 表 4 各属性权重
Table 4. Weight of different attributes
属性 a1 a2 a3 a4 a5 a6 权重 0.0286 0.0963 0.0963 0.1808 0.3058 0.2922 表 5 离散化数据
Table 5. Data after discretization
目标 a1 a2 a3 a4 a5 a6 t1 2 3 3 4 4 4 t2 2 3 2 3 1 3 t3 4 4 1 3 1 4 t4 4 4 4 3 4 1 t5 1 1 3 1 3 1 t6 1 1 4 2 1 2 表 6 决策辨识矩阵
Table 6. Decision identification matrix
目标 a1 a2 a3 a4 a5 a6 t1 Ø a3a4a6 Ø a1a2a3a4 a1a2a4a6 a1a2a3a4a6 t2 a3a4a6 Ø a1a2a3 a1a2a3a6 a1a2a3a4a6 a1a2a3a4 t3 Ø a1a2a3 Ø a3a6 a1a2a3a4a6 a1a2a3a4 t4 a1a2a3a4 a1a2a3a6 a3a6 Ø Ø a1a2a4a6 t5 a1a2a4a6 a1a2a3a4a6 a1a2a3a4a6 Ø Ø a3a4a6 t6 a1a2a3a4a6 a1a2a3a4 a1a2a3a4 a1a2a4a6 a3a4a6 Ø 表 7 约简后的决策系统
Table 7. Decision system after reduction
目标 a1 a3 a6 D t1 2 3 1 4 t2 2 2 1 3 t3 4 1 1 4 t4 4 4 4 1 t5 1 3 3 1 t6 1 4 3 2 表 8 各属性指标下的决策属性权重值
Table 8. Weighted value of decision attribute under different attribute indexes
目标 a1 a3 a6 D t1 0.5 0.5 0.67 1 t2 0.5 1 0.67 1 t3 0.5 1 0.67 1 t4 0.5 0.5 1 1 t5 0.5 0.5 0.5 1 t6 0.5 0.5 0.5 1 表 9 各目标威胁值
Table 9. Threat value of different targets
目标 威胁值 t1 0.5640 t2 0.6122 t3 0.6122 t4 0.6604 t5 0.5144 t6 0.5144 -
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