基于面板数据的灰色四面体网格关联分析模型及应用  

Grey tetrahedral grid incidence analysis model based on panel data and its application

作　　者：吴鸿华 刘思峰[1] 方志耕[1] WU Hong-hua;LIU Si-feng;FANG Zhi-geng(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China;School of Mathematical Sciences,University of Jinan,Jinan 250022,China)

机构地区：[1]南京航空航天大学经济与管理学院,南京211106 [2]济南大学数学科学学院,济南250022

出　　处：《控制与决策》2022年第11期3033-3041,共9页Control and Decision

基　　金：国家自然科学基金项目(72071111,71801127,71671091);国家自然科学基金与英国皇家学会国际合作交流项目(71811530338);国家科技部科技创新引智基地项目(G20190010178);中国博士后科学基金特别资助项目(2019TQ0150);中央高校基本科研业务费专项基金项目(NC2019003,XBA19003)。

摘　　要：针对现有面板数据关联分析模型中指标的排列顺序变换引起灰色关联序不一致以及面板数据三角曲面构造的不足,提出一种基于面板数据的灰色四面体网格关联分析模型.首先,基于数列的组合原理将样本矩阵分解为二元指标子矩阵;其次,将二元指标子矩阵投射为空间四面体网格,并给出四面体的有向体积;然后,基于有向体积构造二元指标的关联系数,最终得到灰色四面体网格关联分析模型,并对模型的对称性、规范性、平移不变性等性质进行证明;最后,将模型应用到山东省沿海城市的空气质量评价,验证模型的合理性和有效性,并分析了灰色四面体网格关联分析模型不受指标排列顺序变化的影响.A grey tetrahedral grid incidence analysis model based on panel data is proposed for the inconsistency of grey incidence order resulting from an order changing of indicators in the grey incidence model and the deficiency of the construction of trigonometric surface for panel data.Firstly,the sample matrix is decomposed into binary indicator sub-matrixes based on the combination principle of sequence.Then,the binary indicator sub-matrix is projected into a spatial tetrahedral grid and the directed volume of the tetrahedroid is given.Based on the directed volume,the incidence coefficient of the binary indicators is constructed.And then,the grey tetrahedral grid incidence analysis model is obtained.Furthermore,the properties of the model including symmetry,normalization,translation-invariance are verified.As a result,the model is used to assess the air quality of coastal cities in Shandong province verifying the rationality and effectiveness of the model,showing that the grey tetrahedron grid incidence analysis model is not related to the order changing of indicators.

关 键 词：面板数据 关联度 灰色关联分析 灰色系统理论 四面体 

分 类 号：N941.5[自然科学总论—系统科学]