关联度公理的简化与特殊关联度的公理化定义

本文首先逐条评价了现有关联度四公理的意义,指出规范性和接近性是必不可少的,整体性和偶对对称性是没有必要的,接近性需要用严谨数学语言描述,适用范围没有必要局限在系统特征序列与相关因素序列之间.规定方式既可以通过两序列直接规定关联度,又可以先规定对应坐标之间的关联系数再规定关联度.然后给出了两类有实际应用背景的特殊关联度的公理化定义,并分别给出了实际例子,为针对不同实际背景规定相应关联度提供了可借鉴的参考方法.

The simplified relational axioms and the axiomatic definition of special incidence degrees

The significance of four axioms of grey incidence degree was evaluated respectively in this paper. It pointed out that the normality and the proximity are essential, the wholeness and the parity symmetry are not necessary, and the proximity needs to be described in rigorous mathematical language, and the applicable scope is not necessarily limited to system characteristic sequence and related factor sequences. There are two ways of providing incidence degree, directly by the two series or by firstly providing incidence coefficients of the corresponding coordinates. Furthermore, the axiomatic definitions of the two special incidence degrees of practical application background and the corresponding actual examples are given in this paper, in order to offer reference methods for providing the corresponding incidence degrees according to different practical background.