基于面板数据的灰色四面体网格关联分析模型及应用
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作者单位:

1、南京航空航天大学,2、济南大学;2.南京航空航天大学

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TP941.5

基金项目:

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(2019TQ0150);中央高校基本科研业务费专项基金资助项目(NC2019003,XBA19003)


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

1、 Nanjing University of Aeronautics and Astronautics,2、University of Jinan

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    摘要:

    针对现有面板数据关联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. 为此, 首先基于数列的组合原理将面板数据所 对应的矩阵分解为二元指标子矩阵. 然后将二元指标子矩阵投射为空间四面体网格, 并给出了四面体的有向体 积. 其次, 基于有向体积构造了二元指标的关联系数, 最终加权平均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了证明. 最后将模型应用到山东省沿海城市的空气质量评价, 验证了 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.

    Abstract:

    A grey tetrahedral grid incidence analysis model based on the panel data is presented for the inconsistency of grey relation order resulting from order changing of indicators in the grey incidence model and the deficiency of the construction of trigonometric surface for panel data. Firstly, the matrix for panel data is split into binary indicator sub-matrix based on the combination principle of sequence. Then, the binary indicator sub-matrix is projected into a spatial tetrahedron grid and the directed volume of the tetrahedron is given. Based on the directed volume, the incidence coefficient of the binary indicators is constructed. Furthermore, we propose the grey tetrahedral grid incidence analysis model and symmetry, normalization, and translation invariance of the model are verified. As a result, the model is applied to the air quality assessment 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.

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  • 收稿日期:2021-04-29
  • 最后修改日期:2021-08-13
  • 录用日期:2021-08-18
  • 在线发布日期: 2021-09-01
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