基于数据分布特征的分层无量纲化方法及其均衡性分析

doi:10.12068/j.issn.1005-3026.2023.06.017

摘要/Abstract

摘要： 分层无量纲化方法能够有效去除指标量纲影响的同时解决异常指标造成的数据分布不均衡、区分度低等问题.然而，该方法的使用需要人为指定区间数，使得无量纲化结果受人为因素的干扰，失去客观性.针对该问题，考虑原始数据的分布特征，提出了密度分层无量纲化方法.该方法按照数据分布的疏密程度进行区间划分，客观确定分层级数，同时兼顾分层无量纲化方法的优点，计算相对简单且减少了人为干扰.此外，通过随机模拟发现，该方法对于异常值具有较好的抗干扰性，且无量纲化结果的均衡性受原始数据规模影响.

关键词: 无量纲化方法；异常值；分层无量纲化方法；数据密度；客观分层

Abstract: The hierarchical dimensionless method can effectively remove the effect of different index dimensions， and solve imbalanced data distribution and low discrimination caused by anomalous index values. However， when using this method， it is necessary to artificially specify the number of partition intervals so that the dimensionless results are interfered by human factors and lose objectivity. To solve this problem， a dimensionless method of density hierarchy is proposed considering the distribution characteristics of raw data. This method divides the interval according to the density of data distribution， objectively determines the hierarchical series， and takes into account the advantages of the hierarchical dimensionless method. The calculation is comparatively simple and reduces human factors. In addition， through the stochastic simulation method， it is found that the method has good anti-interference to outliers， and the balance of dimensionless results is affected by the scale of raw data.

Key words: dimensionless method; outlier; hierarchical dimensionless method; data density; objective hierarchy

中图分类号:

C934

易平涛，袁建荣，李伟伟. 基于数据分布特征的分层无量纲化方法及其均衡性分析[J]. 东北大学学报（自然科学版）, 2023, 44(6): 889-897.

YI Ping-tao， YUAN Jian-rong， LI Wei-wei. Hierarchical Dimensionless Method Based on Data Distribution Characteristics and Its Equilibrium Analysis[J]. Journal of Northeastern University(Natural Science), 2023, 44(6): 889-897.

参考文献

[1]Chen Y，Li W W，Yi P T.Evaluation of city innovation capability using the TOPSIS-based order relation method: the case of Liaoning Province，China［J］.Technology in Society，2020，63: 101330.
[2]Dong Q K，Yi P T，Li W W，et al.Evaluation of city sustainability using the HGRW method: a case study of urban agglomeration on the West Side of the Straits，China［J］.Journal of Cleaner Production，2022，358: 132008.
[3]Chao X R，Kou G，Peng Y，et al.Large-scale group decision-making with non-cooperative behaviors and heterogeneous preferences: an application in financial inclusion［J］.European Journal of Operational Research，2021，288(1):271-293.
[4]Carli R，Dotoli M，Pellegrino R.Multi-criteria decision-making for sustainable metropolitan cities assessment［J］.Journal of Environmental Management，2018，226: 46-61.
[5]Zhang Z G，Hu X，Liu Z T，et al.Multi-attribute decision making: an innovative method based on the dynamic credibility of experts［J］.Applied Mathematics and Computation，2021，393: 125816.
[6]Li W W，Yi P T，Li L Y.Superiority-comparison-based transformation，consensus，and ranking methods for heterogeneous multi-attribute group decision-making［J］.Expert Systems with Applications，2023，213: 119018.
[7]Liu Y T，Sun Z W，Liang H M，et al.Ranking range model in multiple attribute decision making: a comparison of selected methods［J］.Computers & Industrial Engineering，2021，155: 107180.
[8]Mohammadi M，Rezaei J.Ensemble ranking: aggregation of rankings produced by different multi-criteria decision-making methods［J］.Omega，2020，96: 102254.
[9]郭亚军，易平涛.线性无量纲化方法的性质分析［J］.统计研究，2008，25(2):93-100.(Guo Ya-jun，Yi Ping-tao.Character analysis of linear dimensionless methods［J］.Statistical Research，2008，25(2):93-100.)
[10]易平涛，张丹宁，郭亚军，等.动态综合评价中的无量纲化方法［J］.东北大学学报(自然科学版)，2009，30(6):889-892.(Yi Ping-tao，Zhang Dan-ning，Guo Ya-jun，et al.Study on dimensionless methods in dynamic comprehensive evaluation［J］.Journal of Northeastern University(Natural Science)，2009，30(6):889-892.)
[11]胡永宏.对统计综合评价中几个问题的认识与探讨［J］.统计研究，2012，29(1):26-30.(Hu Yong-hong.Understanding and discussion of some problems in statistical synthesis evaluation［J］.Statistical Research，2012，29(1):26-30.)
[12]Li W W，Yi P T，Zhang D N.Investigation of sustainability and key factors of Shenyang City in China using GRA and SRA methods［J］.Sustainable Cities and Society，2021，68: 102796.
[13]Lama N，Boracchi P，Biganzoli E.Exploration of distributional models for a novel intensity-dependent normalization procedure in censored gene expression data［J］.Computational Statistics & Data Analysis，2009，53(5):1906-1922.
[14]Chakraborty S，Yeh C H.A simulation comparison of normalization procedures for TOPSIS［C］//International Conference on Computers & Industrial Engineering.Troyes: IEEE，2009: 1815-1820.
[15]Chen Y，Zhang D N.Evaluation and driving factors of city sustainability in Northeast China: an analysis based on interaction among multiple indicators［J］.Sustainable Cities and Society，2021，67: 102721.
[16]Altintas K，Vayvay O，Apak S，et al.An extended GRA method integrated with fuzzy AHP to construct a multidimensional index for ranking overall energy sustainability performances［J］.Sustainability，2020，12(4):1602.
[17]Awasthi A，Omrani H，Gerber P.Investigating ideal-solution based multicriteria decision making techniques for sustainability evaluation of urban mobility projects［J］.Transportation Research Part A: Policy and Practice，2018，116: 247-259.
[18]李伟伟，易平涛，李玲玉.综合评价中异常值的识别及无量纲化处理方法［J］.运筹与管理，2018，27(4):173-178.(Li Wei-wei，Yi Ping-tao，Li Ling-yu.Outliers recognition and the dimensionless method in comprehensive evaluation［J］.Operations Research and Management Science，2018，27(4):173-178.)
[19]易平涛，李伟伟，李玲玉.序比例诱导分段无量纲化方法及其影响因素［J］.系统管理学报，2020，29(5):866-873.(Yi Ping-tao，Li Wei-wei，Li Ling-yu.A segmented dimensionless method induced by ranking percentage and its influencing factors［J］.Journal of Systems & Management，2020，29(5):866-873.)
[20]易平涛，李伟伟，郭亚军.线性无量纲化方法的结构稳定性分析［J］.系统管理学报，2014，23(1):104-110.(Yi Ping-tao，Li Wei-wei，Guo Ya-jun.Structure stability analysis of linear dimensionless methods［J］.Journal of Systems & Management，2014，23(1):104-110.)
[21]张敏，袁辉.拉依达(PauTa)准则与异常值剔除［J］.郑州工业大学学报，1997(1):87-91.(Zhang Min，Yuan Hui.The PauTa criterion and rejecting the abnormal value［J］.Journal of Zhengzhou University of Technology，1997(1):87-91.)