基于核和灰度的区间灰数运算法则

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基于核和灰度的区间灰数运算法则

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. 作者: 刘思峰方志耕谢乃明 Author: LIU Si-fengFANG Zhi-gengXIE Nai-ming 作者单位: 南京航空航天大学灰色系统研究所,江苏,南京,210016 期 刊: 系统工程与电子技术 ISTICEIPKU Journal: SYSTEMS ENGINEERING AND ELECTRONICS 年,卷(期): 2010,32(2) 分类号: C931 N941.5 关键词: 区间灰数 核 灰度 运算法则 Keywords: interval grey numbers Kernel the degree of greyness of grey numbers algorithm rules 机标分类号: C93 O15 机标关键词: 灰数灰度区间灰数运算法则basedinterval grey numbersrules ofKernel数运算the grey systemdifferential equationtheoretical basis灰色系统灰色微分方程significancedegree运算性质投入产出理论基础理论发展矩阵运算 基金项目: 国家自然科学基金,哈尔滨工业大学校科研和教改项目,人文社会科学规划基金,江苏省高等学校优秀创新团队基金,南京航空航天大学创新群体,特聘教授科研创新基金
基于核和灰度的区间灰数运算法则

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