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摘要:
针对在确定空战威胁评估指标权重时，未考虑指标间的耦合性以及客观赋权法不能从逻辑视角体现指标相对评价对象真正的重要程度的问题，提出了一种基于灰色关联度、灰色关联深度的极大熵模型初步确定权值，再根据指标间灰色关联度以及确定的解耦阈值修正权值的方法。为了克服灰色关联分析法（GRA）和理想点接近法（TOPSIS）的缺点，提出了一种基于GRA-TOPSIS的目标威胁评估方法。首先，通过实例对比分析了指标采用数学模型与模糊处理后，对目标威胁评估结果的影响；其次，对比分析了采用GRA、TOPSIS以及GRA-TOPSIS、数学模型得出的目标威胁评估结果；最后，考虑不同决策者的主观偏好，得出不同的目标威胁评估结果。通过仿真验证了所提方法的有效性以及科学性。
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关键词:
- 灰色关联深度 /
- 指标间灰色关联度 /
- 灰色关联分析法-理想点接近法(GRA-TOPSIS) /
- 极大熵 /
- 分辨系数
Abstract:In order to solve the problem that the coupling between indexes is not considered an the objective weighting method cannot reflect the true importance of indexes relative to evaluation objects from a logical perspective when calculating the weight of indexes in air combat threat assessment, a maximum entropy model based on grey relational degree and grey relational depth is proposed to determine the initial weight, and then the weight is modified according to the grey relational degree among indexes and the decoupling threshold. In order to overcome the shortcomings of grey relational analysis (GRA) and technique for order preference by similarity to solution (TOPSIS), a method of target threat assessment based on GRA-TOPSIS is proposed. First, the influence of mathematical model and fuzzy processing on the target threat assessment is analyzed through example. Second, the results of the target threat assessment using the GRA, TOPSIS, GRA-TOPSIS and mathematical models are compared and analyzed. Finally, different target threat assessment results are obtained by considering the subjective preference of different decision makers. Simulation proved the effectiveness and scientificity of the proposed method.
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图 3 四种方法相对贴近度对比
Figure 3. Comparison of relative nearness degree calculated by four methods
表 1 敌机的参数信息
Table 1. Enemy aircraft parameter information
目标 机型 作战意图 qB/(°) qR/(°) rr/km vr/(m·s-1) 1 F-16C 攻击 80 -45 50 300 2 F-16C 掩护 45 -45 70 325 3 F-5E 攻击 -60 80 60 320 4 F-15E 干扰 -45 15 60 330 
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表 2 灰色关联度
Table 2. Grey relational degree
敌机编号 正理想解灰色关联度 负理想解灰色关联度 相对贴近度 1 0.815 8 0.616 7 0.547 7 2 0.633 1 0.725 3 0.444 1 3 0.783 4 0.605 4 0.542 2 4 0.593 7 0.746 7 0.421 2
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表 3 欧氏距离
Table 3. Euclidean distance
敌机编号 正理想解欧氏距离 负理想解欧氏距离 TOPSIS方法欧氏距离 1 0.353 6 0.629 1 0.394 4 2 0.529 3 0.424 5 0.590 9 3 0.330 3 0.604 1 0.387 8 4 0.543 0 0.521 3 0.546 9
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表 4 无量纲化处理及威胁排序(α=0.5, β=0.5)
Table 4. Dimensionless processing and threat sorting(α=0.5, β=0.5)
敌机编号 正理想解灰色关联度 负理想解灰色关联度 正理想解欧氏距离 负理想解欧氏距离 正理想解贴近度 负理解贴近度 相对贴近度 威胁排序 1 1.000 0 0.825 9 0.651 2 1.000 0 1.000 0 0.738 6 0.574 2 2 2 0.776 0 0.971 4 0.974 7 0.674 9 0.725 5 0.973 1 0.427 1 4 3 0.960 3 0.810 8 0.608 3 0.960 3 0.960 3 0.709 6 0.575 1 1 4 0.727 7 1.000 0 1.000 0 0.828 6 0.778 2 1.000 0 0.437 6 3
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表 5 四种方法相对贴近度与威胁排序比较
Table 5. Comparison of relative nearness degree and threat sorting of four methods
敌机编号 TOPSIS GRA GRA-TOPSIS 数学模型 相对贴近度 威胁排序 相对贴近度 威胁排序 相对贴近度 威胁排序 相对贴近度 威胁排序 1 0.394 4 3 0.547 7 1 0.574 2 2 0.610 7 1 2 0.590 9 1 0.444 1 3 0.427 1 4 0.593 0 2 3 0.387 8 4 0.542 2 2 0.575 1 1 0.487 1 3 4 0.546 9 2 0.421 2 4 0.437 6 3 0.452 1 4
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表 6 α，β不同取值时目标威胁排序
Table 6. Target threat sorting at different values of α, β
敌机编号 α=0.2，β=0.8 α=0.4，β=0.6 α=0.7，β=0.3 正理想解贴近度 负理想解贴近度 相对贴近度 正理想解贴近度 负理想解贴近度 相对贴近度 正理想解贴近度 负理想解贴近度 相对贴近度 1 1.000 0 0.825 9 0.547 7 1.000 0 0.756 0 0.569 5 1.000 0 0.703 6 0.575 2 2 0.776 0 0.971 4 0.444 1 0.735 6 0.972 7 0.430 6 0.705 2 0.973 7 0.420 2 3 0.960 3 0.810 8 0.542 2 0.960 3 0.729 8 0.568 2 0.960 3 0.669 1 0.575 1 4 0.727 7 1.000 0 0.421 2 0.768 1 1.000 0 0.434 4 0.798 4 1.000 0 0.443 9 排序 1>3>2>4 1>3>4>2 1>3>4>2
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