【作者】 姜晓；

【导师】 范周田；

【作者基本信息】 北京工业大学 ， 应用数学， 2007， 硕士

【摘要】 本文利用图论方法研究了格矩阵幂序列的性质。我们从模糊集与模糊关系的概念开始，引出模糊矩阵幂序列的收敛性问题。然后针对中外学者研究成果中区间问题，把模糊矩阵幂序列的研究推广到格矩阵上。格矩阵的分解定理，是联系格矩阵和布尔矩阵之间的桥梁。本文主要研究格矩阵的有向伴随图，得到了收敛格矩阵的图论特征，进而得到了格矩阵收敛的一些充要条件以及幂敛指数的计算方法。本文建立的有关结果可以视为对以往关于模糊矩阵幂序列的收敛性的研究成果的发展，为格矩阵应用于神经网络等领域解决了收敛性问题。更多还原

【Abstract】 This paper researched on the convergence of lattice matrices using graphtheoretical approach. At first, both the concepts of fuzzy set and fuzzy re-lation are given, and the convergence of fuzzy matrices is introduced. Thenwe stressed the interval question of the previous research and extended theresearch of fuzzy matrix to the research of lattice matrix.The decomposition theorem of lattice matrix builds the bridge betweenlattice matrices and Boolean matrices.This paper mainly researched on thedirected graph of lattice matrices,and got the gragh-theoritical characteris-tic of the convergent lattice matrices, then got some sufficient and necessaryconvergent conditions of lattice matrices and the method of computing theconvergence index.The results presented could be regarded as the development of the previ-ous research on fuzzy matrix.And the convergence problem is basically resolvedfor lattice matrix applying to the fields of nerve network.更多还原