基于核和灰度的区间灰数运算法则

Journal of Systems Engineering and Electronics ›› 2010, Vol. 32 ›› Issue (2): 313-316.

基于核和灰度的区间灰数运算法则

刘思峰, 方志耕, 谢乃明

（南京航空航天大学灰色系统研究所, 江苏南京 210016）

出版日期:2010-02-03 发布日期:2010-01-03

Algorithm rules of interval grey numbers based on the “Kernel” and
the degree of greyness of grey numbers

LIU Si-feng, FANG Zhi-geng, XIE Nai-ming

(Inst. for Grey Systems, Nanjing Univ. of Aeronautics and Astronautics, Nanjing 210016, China)

Online:2010-02-03 Published:2010-01-03

摘要/Abstract

摘要：

区间灰数运算是灰色系统的理论基础，对灰色系统理论发展的影响举足轻重。首先给出了灰数“核”的定义，基于“核”和灰数灰度建立了区间灰数运算公理、运算法则和新的灰代数系统，并研究了运算性质。至此，灰数运算被转化为实数运算，区间灰数运算的难题在一定程度上得到解决。定义的区间灰数运算可以推广到以区间灰数为基本元素的灰色代数方程、灰色微分方程、灰色矩阵运算的情形，而且有助于由于受到区间灰数运算困难的制约一直进展缓慢的灰色投入产出和灰色规划等方面的研究。

Abstract:

The algorithm of interval grey numbers is the theoretical basis of a grey system theory. It has very important significance in developing the grey system theory. A definition of “Kernel” is given first. Algorithm axioms, algorithm rules of interval grey numbers and new algebraic systems are built based on the “Kernel” and the degree of greyness of grey numbers. And the properties of the algorithm are studied. Up to now, the algorithm of interval grey numbers are transformed to the algorithm of real numbers, so the difficult problem for algorithm of interval grey numbers is solved to a certain degree. The algorithm of interval grey numbers is extended to the grey algebraic equation, grey differential equation and grey matrix algorithm including interval grey numbers. The algorithm system of interval grey numbers is helpful for research on grey inputoutput and grey programming.

刘思峰, 方志耕, 谢乃明. 基于核和灰度的区间灰数运算法则[J]. Journal of Systems Engineering and Electronics, 2010, 32(2): 313-316.

LIU Si-feng, FANG Zhi-geng, XIE Nai-ming. Algorithm rules of interval grey numbers based on the “Kernel” and
the degree of greyness of grey numbers[J]. Journal of Systems Engineering and Electronics, 2010, 32(2): 313-316.