PDF《分层构权灰色主成分评价模型及其应用》

第34卷第6期 控制与决策Vol.

34 No.6 2019年 6月 Control and Decision Jun.

2019 文章编号: 1001-0920(2019)06-1300-07 DOI: 10.13195/j.kzyjc.2017.1405 分层构权灰色主成分评价模型及其应用 王玲玲1,2? , 方志耕1 (1. 南京航空航天大学 经济与管理学院,南京 211106;

2. 江苏大学 财经学院,江苏 镇江 212013) 摘要: 针对评价实践中客观存在的 原始变量不多 与 样本量不多 ,构建分层构权灰色主成分评价模型. 首先,在科学设置评价子系统及下属指标项的前提下,分层赋予相应归一化重要性权;

其次,生成评价所需的加权规 格化矩阵,据此计算灰色相似关联度矩阵,替代相关系数矩阵求解评价样本各子系统的主成分综合得分;

然后,将 所得分值按各子系统重要性权进一步合成得出最终评价依据;

最后,结合火电机组性能综合评价实例,对不同评价 方法得出的评价实际效果进行对比分析. 理论研究与案例分析论证表明,对于评价实践中存在的少变量、 小样本 以及评价指标间不一定满足线性相关关系的情形,分层构权灰色主成分评价模型具备科学性、 有效性和较优的适 用性. 关键词: 灰色相似关联度;

分层构权;

主成分评价;

灰色评价;

多指标评价;

火电机组 中图分类号: C81 文献标志码: A Multi-layer weighted grey principal component evaluation model and its application WANG Ling-ling1,2? , FANG Zhi-geng1 (1. College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 211106, China;

2. Department of Economics,Jiangsu University,Zhenjiang 212013,China) Abstract: Considering the lack of primitive variables and samples, which exists objectively in the evaluation practice, the multi-layer weighted grey principal component evaluation model is constructed. Firstly, the normalized importance weights are assigned to the subsystem of the evaluation system and the corresponding indices respectively under the premise that all of them are established scienti?cally. On that basis, the weighted normalized matrix for evaluation is generated to calculate the grey similitude correlation degree matrix, and the principal component scores of each evaluation subsystem are calculated based on it instead of the traditional correlation matrix. Then, the ?nal evaluation basis is obtained through weighting the scores of each evaluation subsystem by their importance weights. Finally, performances of thermal power generation units are analyzed comparatively by using di?erent evaluation models including the proposed model. Theoretical research and case analysis demonstrate that the proposed model is scienti?c, e?ective and more suitable in these situations where there are insu?cient evaluation variables, or the sample size is small, as well as there may be a non-linear correlation between evaluation indicators. Keywords: similitude degree of grey incidence;

multi-layer weighted;

principal component evaluation;

grey evaluation;

multi-index evaluation;

thermal power generation unit

0 引言主成分分析法操作方便[1] ,其降维思想与多指标 评价指标序化的要求十分契合[2] , 是目前应用最为 广泛的降维方法之一[3] . 但是一些学者同时也指出, 主成分分析法的应用受一定条件限制: 1) 原始变量 不多、数据结构比较简单的问题不适合用主成分分 析[4] ;

2)主成分是原始指标的线性组合,因而它是一 种 线性 降维技术,只能处理线性问题[1,5] ;