基于核和灰度的区间灰数的序关系

首先,根据区间灰数的核的概念,在同核区间灰数定义的基础上,讨论了基于核的区间灰数的等价关系和大小关系,并给出了一系列相关结论。其次,根据区间灰数的灰度的概念,在同灰度区间灰数定义的基础上,讨论了基于灰度区间灰数的等价关系和大小关系,也得到了一系列相关结论。最后,在同时考虑核和灰度的基础上,讨论了区间灰数的序关系,并得到区间灰数的偏序关系不是全序关系的结论,从而说明基于核和灰度的区间灰数代数系统不能定义大小关系,同时这也说明了基于核和灰度的灰数表示形式具有一定的局限性。

ORDERING RELATIONS OF INTERVAL GREY NUMBERS BASED ON THE KERNEL AND THE DEGREE OF GREYNESS OF GREY NUMBERS

Firstly,according to the kernel of grey numbers,the definition of identical kernel of the interval grey number is given in this paper. And then the concept of equivalence relation and magnitude relation based on the identical kernel of grey numbers are defined and followed by a series of theorems. Secondly,based on identical degree of greyness of the interval grey number defined in this paper,the concept of equivalence relation and magnitude relation based on the identical degree of greyness of the interval grey numbers are defined and is followed by a series of theorems. Lastly,by taking the kernel and the degree of greyness of grey numbers into consideration,this paper defines several ordering relation,and partial relation cannot form total ordering relation,and this conclusion demonstrate that algebraic system of interval grey number based on the kernel and degree of greyness cannot define magnitude relation of internal grey numbers and this expression of internal grey numbers have its limitations.