基于判别精度最优的KNN-BWM评价模型  

KNN-BWM Evaluation Model Based on Discriminant Accuracy Optimization

作　　者：梅晗 李战江[1] 种政 MEI Han;LI Zhan-jiang;CHONG Zheng(College of Economics and Management,Inner Mongolia Agricultural University,Hohhot 010010,China)

机构地区：[1]内蒙古农业大学经济管理学院,内蒙古呼和浩特010010

出　　处：《数学的实践与认识》2025年第3期39-51,共13页Mathematics in Practice and Theory

基　　金：国家自然科学基金“复杂信息融合下家庭农牧场的动态组合信用评级研究-以内蒙古为例”(72161033)。

摘　　要：研究从二分类判别精度最优的角度出发构建了一种评价模型,用于衡量被评价对象的性能优劣.首先构建了基于K近邻(KNN)-最优最劣法(BWM)组合赋权的评分模型;然后以同一等级内评分差距小、不同等级内评分差距大为原理建立目标函数、以不同等级内样本数服从“中间多、两边少”原则为约束条件建立非线性规划模型对样本划分等级;最后以内蒙古722个家庭农牧场为数据来源对模型进行应用.创新点:一是以正确判别二分类状况样本占总样本比重的方式计算单个指标的判别准确度,再依据单个指标判别准确度占全部指标判别准确度的比重计算单个指标的客观权重,体现了“判别精度越大的指标越重要”这一赋权思想,不仅解决了利用常规客观赋权方法计算指标权重时无法辨别分类能力强的指标这一问题,还解决了单纯采用KNN法进行二分类判别时可解释性差的问题;二是以判别二分类正确的样本数与全部样本数之比最大为目标函数构建非线性规划模型,反推客观权重与主观权重的最优占比系数以进行组合赋权,解决了现有组合赋权方法未能使二分类判别效果达到最优的问题J-T检验结果表明:所构建的基于判别精度最优的评价模型具有合理性;对比分析结果表明:所构建的等级划分模型更能兼顾样本差异与各等级下的样本数量分布情况.In this study,an evaluation model is constructed from the perspective of optimal binary classification discriminant accuracy to measure the performance advantages and disadvantages of the evaluated objects.We first constructed a scoring model based on the combination of KNN-BWM;then we established an objective function based on the principle that the difference in scores within the same grade is small and the difference in scores within different grades is large,and a nonlinear programming model is established based on the constraint that the number of samples within different grades obeys the principle of"more in the middle and less on the sides"to classify the samples into grades;finally,the credit rating of 722 family farms in Inner Mongolia is used as a case study to apply the model.The innovations of this study are:firstly,the discriminating accuracy of individual indexes is calculated by the proportion of corectly discriminated second-classified status samples to the total samples,and then the objective weights of individual indexes are calculated according to the proportion of the discriminating accuracy of individual indexes to the discriminating accuracy of all indexes,which embodies the idea of"the more important the indexes with higher discriminating accuracy are".It not only solves the problem of not being able to identify indicators with strong classification ability when calculating indicator weights using conventional objective weighting methods,but also solves the problem of poor interpretability when using the KNN method for binary classification;secondly,it constructs a nonlinear programming model with the ratio of the number of samples correctly classified in binary classification to the maximum of all samples as the objective function,and then inversely pushes forward the optimal ratio coefficients of the objective and subjective weights to carry out combined weighting,which solves the problem that existing combination assignment methods fail to optimize the effect of binary classification dis

关 键 词：光判别精度 K近邻 最优最劣法 组合赋权 

分 类 号：F224.0[经济管理—国民经济] F224.5