基于max-product复合的模糊矩阵幂序列的收敛性及其分类  

Convergence and Detailed Classification of Powers of a Fuzzy Matrix under the Max-product Composition

作　　者：焦烨[1] 

机构地区：[1]西安邮电学院应用数学与应用物理系,陕西西安710061

出　　处：《模糊系统与数学》2007年第1期97-105,共9页Fuzzy Systems and Mathematics

摘　　要：主要讨论模糊矩阵在max-product复合意义下的收敛性。通过对模糊矩阵元素的有限收敛、无限收敛、有限振荡、无限振荡的情况的讨论,引入模糊矩阵的有限收敛、无限收敛、有限振荡、无限振荡的概念,证明模糊矩阵在m ax-product复合意义下要么有限收敛,要么无限收敛,要么有限振荡,要么无限振荡,给出了模糊矩阵在max-product复合意义下收敛性的完整结论,并澄清已有文献中的一些错误。最后给出基于max-product复合的模糊矩阵幂序列的分类情况。Convergence of the power sequence of an n × n fuzzy matrix under the max-product composition has been studied by definiting finite convergence, infinite convergence, finite oscillation and infinite oscillation of a fuzzy matrix. It is shown that the powers of an n ×n fuzzy matrix under the max-product composition either converge to an idempotent fuzzy matrix with a finite or infinite index, or oscillate with a finite or infinite period. The complete characterization for the convergent theory of the power sequence of a fuzzy matrix under the max-product composition is set up, and some mistakes in the existing reference are pointed out.

关 键 词：模糊矩阵 max-product复合 有限收敛 无限收敛 有限振荡 无限振荡 

分 类 号：O159[理学—数学]