【作者】 王占京；

【导师】 王熙照；

【作者基本信息】 河北大学 ， 基础数学， 2005， 硕士

【摘要】 模糊线性方程组解的研究是模糊代数的一个基础部分,而本论文的核心是研讨一类形如X=AX+U的模糊线性方程组的解以及它的迭代算法,其中未知量X和常量U均是由模糊数组成的向量,而A分三种状态,(ⅰ)n×n实数矩阵,对这种情形的研究构成第二章。(ⅱ)n×n区间数矩阵(即以区间数为元素的矩阵),对此种情形的研讨构成第三章。(ⅲ)n×n模糊数矩阵(即以模糊数为元素的矩阵),对该情形的研究构成第四章。各章探讨的目标类似,主要有两个:(1)方程组解的存在条件:(2)解存在的条件下它的迭代算法及其误差估计。本文中使用的模糊数的加法、乘法、及数乘均是以Zadeh的扩展原理定义的。更多还原

【Abstract】 The study of the solutions to the fuzzy linear equations constitutes an important part of fuzzy algebra. And this thesis takes the study of solutions to a type of fuzzy linear equation set in the form of X=AX+U and the iterate algorithm as the central issue. In this form of equation the unknown quantity X and constant U are both vectors made up of fuzzy numbers, while A may exist in three states: (i) n×n real number matrix and the study of this state constitutes the second chapter; (ii) n×n interval number matrix (i. e. the matrix made up of interval number elements )and the study of this state constitutes the third chapter; (iii) nxn fuzzy number matrix (i. e. the matrix made up of fuzzy number elements) and the study of this state is the subject of the fourth chapter. The subjects of each chapter bear a similarity in two points: (i) the condition in which the equation set has solutions; (ii) when the former condition is fulfilled the iterative algorithm of the equation set and the estimation of its errors. The addition, multiplication and shucheng in this thesis are all defined according to the expansion theory of Zadeh.更多还原