﻿ 基于信息熵和粗糙集的空中目标威胁评估方法<sup>*</sup>
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1. 空军工程大学 航空工程学院, 西安 710038;
2. 空军工程大学 装备管理与安全工程学院, 西安 710051

Threat evaluation method of air target based on information entropy and rough set
YANG Yuanzhi1, ZHOU Zhongliang1, LIU Hongqiang1, KOU Tian1, FAN Xiangyu2
1. Aeronautics Engineering College, Air Force Engineering University, Xi'an 710038, China;
2. Equipment Management and Safety Engineering College, Air Force Engineering University, Xi'an 710051, China
Received: 2017-12-11; Accepted: 2018-02-09; Published online: 2018-03-15 10:16
Foundation item: National Natural Science Foundation of China (61472443)
Corresponding author. ZHOU Zhongliang, E-mail:zzl_panda@163.com
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.
Keywords: air target     surface air defense     rough set (RS)     information entropy (IE)     threat evaluation

1 基于信息熵的目标属性权重计算

1.1 目标属性的确定

1.2 属性权重的计算

 (1)

λ矩阵进行规范化处理，消除空中目标不同属性之间的量纲差异。此步骤需要判定λ矩阵中各属性的性质，划分效益型和成本型，从而得到规范化特征值矩阵R=(rij)m×n

 (2)

 (3)

 (4)

 (5)

 (6)

 (7)

 (8)
1.3 确定权重最大的属性替代决策属性

 (9)

ω0相对应的目标属性即可作为决策属性，将此决策属性和其他条件属性联合，构造粗糙集理论可以处理的威胁评估模型。

2 基于粗糙集的目标威胁评估

2.1 构建决策环境

2.2 离散属性值

 (10)

ZA中的重要性：

 (11)

2.3 属性约简

 (12)

Dd([xi]A, [xj]A)为[xi]A与[xj]A的决策辨识集，称式(13)为决策辨识矩阵：

 (13)

B为决策协调集，∀Dd([xi]A, [xj]A)≠ø，有

 (14)

CB都不为决策协调集，称B为决策约简集。

2.4 计算属性指标下的决策属性的权重表

 (15)

 (16)

 (17)

3 威胁评估处理流程

 图 1 威胁评估模型 Fig. 1 Model of threat evaluation

4 仿真分析

 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

1) 目标类型：小型目标(如巡航导弹)、大型目标(如轰炸机)、直升机依次量化为3、2、1。

2) 目标干扰能力：强、中、弱、无依次量化为4、3、2、1。

3) 目标高度：高、中、低、超低依次量化为4、3、2、1。

 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

 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

 属性 a1 a2 a3 a4 a5 a6 权重 0.0286 0.0963 0.0963 0.1808 0.3058 0.2922

 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

 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

 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

 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

 目标 威胁值 t1 0.5640 t2 0.6122 t3 0.6122 t4 0.6604 t5 0.5144 t6 0.5144

 图 2 仿真决策与样本决策对比 Fig. 2 Comparison between simulation decision and original decision

5 结论

1) 采用信息熵方法计算目标属性权重，选取权重最大的属性替代决策属性，构建完备的粗糙集威胁评估模型，实现对空中多目标的定量评估，拓宽了粗糙集理论的适用范围，解决在决策未知情况下的空中目标威胁评估问题。

2) 粗糙集理论在数据支持的基础上，可以减少人为主观因素的影响，且离散化过程对数据具有一定程度的容错性，易于实现实时精确评估，为地面防空系统进行空中目标威胁评估、合理配置防空资源提供了一种新的工程决策方法。

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#### 文章信息

YANG Yuanzhi, ZHOU Zhongliang, LIU Hongqiang, KOU Tian, FAN Xiangyu

Threat evaluation method of air target based on information entropy and rough set

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(10): 2071-2077
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0768