摘要
在对一个系统进行关联分析时,邓氏灰色关联分析模型常采用的数据预处理算子有初值化算子、均值化算子、逆化算子和倒数化算子。不同算子进行数据预处理后计算的灰色关联度一般不同,研究算子的性质及如何选用成为灰色关联分析模型的重要问题。讨论了初值化和均值化算子之间关系的性质及其在计算灰色关联度中的一些联系,得到邓氏灰色关联度为1关于初值化算子的等价条件和关于均值化算子的充分条件,进而证明了初值化得到的邓氏关联度为1是均值化得到邓氏关联度为1的充分条件,同时证明了逆化算子和均值化算子之间关系的性质。
When analyzing the incidence relationship for some system,the data preprocessing operators commonly used in the Deng’s grey relational analysis model,including initial value operator,mean operator,inverse operator and recip-rocal operator.Different data preprocessing operators will derive different grey relational values and different ranks.It is an important issue to explore the properties of the operators.We discuss the properties concerning the relation between the above two operators and their relation in constructing the grey relational analysis model.We found the necessary and sufficient condition concerning the initial value normalizing operator and the sufficient condition for the grey relational grade value 1.Then,the grey relational grade value 1 derived by the initial value normalizing operator implies the grey relational grade value 1 derived by the mean value normalizing operator.Meanwhile,the properties of the relationship between inversion operator and mean operator are proved.
作者
郭弘
陈勇明
GUO Hong;CHEN Yongming(College of Applied Mathematics,Chengdu University of Information Technology,Chengdu 610225,China)
出处
《成都信息工程大学学报》
2020年第2期235-238,共4页
Journal of Chengdu University of Information Technology
基金
四川省科学技术厅软科学研究计划资助项目(2018ZR 0287)
成都市科学技术局软科学研究项目(2016-RK00-00269-ZF)对本文的资助。
关键词
灰色系统
灰色关联分析
邓氏灰色关联度
初值化算子
均值化算子
逆化算子
倒数化算子
grey system
grey relational analysis
Deng’s grey relational grade
the initial value normalizing operator
the mean value normalizing operator
the inverse operator
the reciprocal operator
