指标无量纲化的性质分析与方法选择  

Property Analysis and Method Selection of the Indexes Being Dimensionless

作　　者：岳立柱[1] 许可[1] 施光磊 YUE Li-zhu;XU Ke;SHI Guang-lei(School of Business Administration,Liaoning Technical University,Huludao 125105,China)

机构地区：[1]辽宁工程技术大学工商管理学院,辽宁葫芦岛125105

出　　处：《统计与信息论坛》2020年第6期3-9,共7页Journal of Statistics and Information

基　　金：国家社会科学基金资助项目“基于宅基地有偿退出的农业转移人口市民化激励机”(17BSH076)。

摘　　要：无量纲化方法影响数据分析结果,选择何种无量纲化函数是现实决策中的一个难题。遵循指标数值需要映射到同一区间的原则,对指标无量纲应具备的性质进行了分析。结果表明:当指标数据映射为[0,1]区间,线性无量纲函数最终归结为统一的表达形式;对任意单调非线性无量纲函数均可以由极差无量纲化函数和生成函数复合表示。采用何种无量纲化方式均不能避免逆向问题,有效确认指标数据端点是避免逆序的关键性步骤。实例分析表明,线性无量纲函数不能完全替代非线性无量纲函数,需要结合问题实际才能合理选择函数形式。Dimensionless method affects the results of data analysis,and it is a difficult problem to select dimensionless function in practical decision-making.With the principle that the index values need to be mapped to the same interval,the property analysis of the indexes being dimensionless is carried out.The results show that when the index data is mapped to the internal between 0 and 1,the linear dimensionless function ultimately comes down to a unified expression.Besides,any monotonic non-linear dimensionless function can be represented compositely by the range dimensionless function and the generation function.Any dimensionless method must face the inverse problem,and the key step is to confirm the endpoint of the index data effectively.The example analysis shows that the linear dimensionless function can’t completely replace the non-linear,and it is necessary to combine the practical problems to reasonably select the function.

关 键 词：无量纲化 单调性指标 适度型指标 逆向指标 

分 类 号：C934[经济管理—管理学]