Decheng Fan, Jon Song, Pang Cholho, Dong Wang, Won CholJin
School of Economics and Management, Harbin Engineering University, Harbin 150001, China.
Department of Physics, University of Science, Pyongyang 950003, Democratic People's Republic of Korea.
Heliyon. 2018 Nov 28;4(11):e00984. doi: 10.1016/j.heliyon.2018.e00984. eCollection 2018 Nov.
Cluster analysis is widely used in fields such as economics, management and engineering. The distance and correlation are two of the most important and often used mathematics- and statistics-based similarity measures in cluster analysis. Many studies have been conducted to improve the distance and similarity in high-dimensional and overlapped data. However, these studies do not consider the degree of influence (weight) of different properties on different types of data. In practice, the weight of each property is different, so these methods cannot accurately analyze real data. First, this study proposes a new distance measure that can reflect the weight, so that non-spherical overlapping data in the Euclidean space can be projected onto a weighted Euclidean space to form non-overlapping data. Second, the Fuzzy-ANP method is used to determine the weight of each factor. Then, by applying the Fuzzy-ANP-Weighted-Distance-QC (FAWQC) method to weighted random data, the effectiveness of the method is verified. Finally, the method is applied to the 2015 Economics-Energy-Environment (3E) data for 19 provinces in China for a comparative study of the classification of the system structure and evaluation of the low-carbon economy development level. The experiment results show that the FAWQC method can more accurately analyze real-world data than other methods.
聚类分析在经济学、管理学和工程学等领域有着广泛应用。距离和相关性是聚类分析中基于数学和统计学的两种最重要且常用的相似性度量。许多研究致力于改进高维数据和重叠数据中的距离与相似性。然而，这些研究未考虑不同属性对不同类型数据的影响程度（权重）。在实际中，每个属性的权重各不相同，因此这些方法无法准确分析真实数据。首先，本研究提出一种能够反映权重的新距离度量，使得欧几里得空间中的非球形重叠数据能够投影到加权欧几里得空间以形成非重叠数据。其次，运用模糊网络分析法确定各因素的权重。然后，通过将模糊网络分析法 - 加权距离 - 质量控制（FAWQC）方法应用于加权随机数据，验证了该方法的有效性。最后，将该方法应用于中国19个省份的2015年经济 - 能源 - 环境（3E）数据，对系统结构分类和低碳经济发展水平评估进行比较研究。实验结果表明，FAWQC方法比其他方法能更准确地分析现实世界数据。
