max-zero t-模复合意义下的模糊矩阵幂序列的收敛性

Convergence of Powers of a Fuzzy Matrix under the max-zreo t-norm Composition

主要讨论模糊矩阵在max-zerot-模(以下简称为max-t0)复合意义下的收敛性。证明了模糊矩阵在max-t0复合意义下只有有限收敛,无限收敛,有限振荡及无限振荡这四种情况。并主要以一种特殊且重要的zerot-模:lukasiewiczt-模为例,研究了max-lukasiewiczt-模(以下简称为max-lu)复合意义下的模糊矩阵的收敛性,证明了在max-lu复合意义下,模糊矩阵要么有限收敛要么有限振荡。且比较了在max-lu复合意义下以及在max-product复合意义下,模糊矩阵收敛性的相同之处与不同之处,并揭示其原因。

<Abstrcat> In this paper, convergence of the power sequence of an n×n fuzzy matrix under the (max-zero) t-norm composition has been studied. It is shown that the powers of an n×n fuzzy matrix under the max-zero t-norm composition either converge to an idempotent fuzzy matrix with a (finite) or infinite index, or oscillate with a finite or infinite period. Then, as an especial and important zero (t-norm:Lukasiewicz t-norm,) the convergent theory of the power (sequence) of a fuzzy matrix under the max-Lukasiewicz t-norm composition is studied. Moreover, note the similarities and differences (between) convergences of the power sequence of an n×n fuzzy matrix under the max-product (composition) and under the max-Lukasiewicz t-norm composition.