基于核和灰度的区间灰数代数系统

Algebraic System of Interval Grey Numbers Based on the "Kernel" and the Degree of Grayscale of Grey Numbers

根据区间灰数的核和灰度的概念,利用灰数的简化形式,从代数学的角度讨论了区间灰数代数系统.首先,讨论了具有简化形式的区间灰数代数系统的算术运算,然后,通过分别为具有加法和乘法的简化形式的区间灰数代数系统引进逆元,从而进一步讨论了区间灰数代数系统的性质,最后,在综合考虑核和灰度的基础上,利用距离为区间灰数进行了分类,建立了区间灰数的相容类.

Based on the ＂Kernel＂,the degree of grayscale of grey numbers and reduced form of grey numbers,algebraic system of interval grey numbers are formulated from algebra angle.Firstly,arithmetic operation of algebraic system of interval grey numbers with reduced form of grey numbers was discussed in this paper;Secondly,by means of definition of inverse elements for addition and multiplication respectively,it enabled algebraic system of interval grey numbers to have more perfect natures.Finally,kernel and grayscale are took into consideration synthetically,and consistent class of interval grey numbers are built by applying distance of Kernel,the degree of grayscale of grey numbers.