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1. 北京航空航天大学 电子信息工程学院, 北京 100083;
2. 中国科学院 数学与系统科学研究院, 北京 100190

Adaptive evaluation method based on analytic hierarchy process
ZHANG Yaotian1 , ZHANG Xucheng2 , JIA Mingshun1 , XUE Xiangshang1
1. School of Electronic and Information Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China ;
2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Received: 2016-01-22; Accepted: 2016-04-08; Published online: 2016-05-25 12: 00
Corresponding author. Tel.:010-82318918 E-mail:zhangyaotian@buaa.edu.cn
Abstract: In order to improve the performance of classical analytic hierarchy process (AHP) which has defects of subjectivity and less quantitative component, at the same time according to the objective information which is implied by a plurality of target data matrix, the classical AHP was modified and a changeable weight evaluation method based on AHP was proposed. The conclusion is that the new method is able to adjust the weights of the evaluative parameter dynamically by analysis of the data distribution. By this way the weight of low discrimination index is reduced while the weight of high discrimination index is improved, which makes the AHP more objective, and to some extent the guiding role of the scarcity index is also reflected. The effectiveness of the new method is verified by using the example of the evaluation of the despeckling algorithm of synthetic aperture radar image.
Key words: analytic hierarchy process (AHP)     changeable weight     evaluation method     scarcity index     despeckling algorithm

1 评价指标集的构建和预处理

A={A1,A2,…,Am}为被评价对象的全体,B={B1,B2,…,Bn}为评价指标的全体。

1.1 评价指标集的构建

1.2 评价值的预处理

 (1)

 (2)
 (3)

2 评价指标的自适应赋权

2.1 层次分析法确权及数据修正

 (4)

 (5)

2.2 权重的自适应修正

 (6)

 (7)

 (8)

 (9)

 (10)

 (11)

 (12)

 (13)

 (14)

2.3 利用加性加权法计算评分

 (15)

3 实例应用

3.1 SAR图像降斑算法评价指标体系

 准则层A 指标层B 指标描述 平滑能力(A1) ENL(B1) 评价均匀区域平滑效果,数值越大,平滑能力越强 细节保留(A2) EPI(B2) 描述细节保存的能力,数值越大,细节信息丢失越少 TCR(B3) 描述点目标的保存能力,数值越大,效果越好 噪声影响(A3) ERI(B4) 描述噪声的分布,数值越接近1,说明越接近Γ分布 PSNR(B5) 数值越大,降噪效果越好(假设每幅图像都能找到原图)

 图 1 SAR图像1及其降斑图像 Fig. 1 Image 1 of SAR and its despeckling images
 图 2 SAR图像2及其降斑图像 Fig. 2 Image 2 of SAR and its despeckling images

 指标 Lee滤波 PPB SAR-BM3D 小波收缩变换 TDST滤波 B1(ENL) 1.747 8 1.100 4 1.527 9 1.471 3 1.458 2 B2(EPI) 0.216 5 0.657 4 0.408 0 0.300 6 0.302 4 B3(TCR) 9.649 9 12.409 7 10.290 0 11.111 9 10.771 2 B4(ERI) 0.971 0 0.998 4 0.838 9 1.055 0 1.082 6 B5(PSNR) 21.272 9 24.000 0 23.703 7 21.894 1 21.932 8

 指标 Lee滤波 PPB SAR-BM3D 小波收缩变换 TDST滤波 B1(ENL) 2.799 7 1.738 9 2.659 1 2.606 3 2.591 7 B2(EPI) 0.119 4 0.675 6 0.097 7 0.138 7 0.142 8 B3(TCR) 8.554 9 12.977 7 9.319 7 10.101 5 9.781 5 B4(ERI) 1.000 5 1.008 4 0.907 5 1.003 4 1.004 3 B5(PSNR) 21.089 2 22.000 0 21.062 5 21.366 3 21.259 9

3.2 评价结果对比及分析

3.2.1 层次分析法和本文方法的权重变化对比分析

 指标 层次分析法权重 本文方法权重 绝对变化 B1(ENL) 0.292 1 0.248 3 -0.043 8 B2(EPI) 0.120 1 0.138 1 0.018 0 B3(TCR) 0.070 5 0.081 1 0.010 6 B4(ERI) 0.101 6 0.086 4 -0.015 2 B5(PSNR) 0.415 7 0.446 2 0.030 5

3.2.2 本文方法对降斑算法的评价结果分析

 算法 图 1(a)评分 图 1(a)排序 图 2(a)评分 图 2(a)排序 Lee滤波 -0.380 240 5 -0.240 830 3 PPB 0.654 673 1 0.505 191 1 SAR-BM3D 0.378 801 2 0.336 952 2 小波收缩变换 -0.290 820 3 -0.260 950 4 TDST滤波 -0.362 410 4 -0.340 360 5

4 结论

1) 本文方法利用被评价群体的指标值修正决策矩阵,因此在评价过程中包含了被评价对象的自身信息,较经典的层次分析法更为客观,特别适用于对算法、方法等处理对象差异性大的对象(如本文中提到的降斑算法评价)的评价或需要考虑在评价结果中体现政策、时间等因素影响的评价过程(如绩效评估)。

2) 指标值分布相对集中时,将降低该指标的基础权重;被评价个体在某指标值较被评价群体有明显优势时,将提升该指标的基础权重。从而有效体现稀缺性指标在评价体系中的导向作用。

3) 指标权重修正幅度不大,在可接受范围内,由专家主观判断产生的指标权重在决策评价过程中仍然占据主导地位。

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#### 文章信息

ZHANG Yaotian, ZHANG Xucheng, JIA Mingshun, XUE Xiangshang

Adaptive evaluation method based on analytic hierarchy process

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(5): 1065-1070
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0224