Abstract: The notion of [n]-fold fuzzy implicative filter of a [BL]-algebra is introduced and some properties of a [n]-fold fuzzy implicative filter are investigated, several equivalent conditions of a [n]-fold fuzzy implicative filter are also given. At the same time, a simple condition to verify whether or not a fuzzy filter is a [n]-fold fuzzy implicative filter is also given. Furthermore, it is proved that [n]-fold implicative [BL]-algebra is characterized by a [n]-fold fuzzy implicative filter and a fuzzy filter is a [n]-fold fuzzy implicative filter if and only if the corresponding quotient is a [n]-fold implicative[BL]-algebra.

Key words: [BL]-algebra, fuzzy filter, [n]-fold fuzzy implicative filter, [n]-fold implicative [BL]-algebra

摘要： 引入[BL]-代数的[n]-重模糊蕴涵滤子概念，讨论了[n]-重模糊蕴涵滤子的性质，给出若干等价刻画，给出了验证[n]-重模糊蕴涵滤子的一个简单条件。用[n]-重模糊蕴涵滤子对[n]-重蕴涵[BL]-代数进行了刻画，证明了一个模糊滤子是一个[n]-重模糊蕴涵滤子当且仅当对应的商代数是一个[n]-重蕴涵[BL]-代数。

关键词: [BL]-代数, 模糊滤子, [n]-重模糊蕴涵滤子, [n]-重蕴涵[BL]-代数