MTL代数的蕴涵滤子与正蕴涵滤子

Implicative filters and positive implicative filters of MTL algebras

在MTL代数M上引入了蕴涵滤子、正蕴涵滤子的概念,研究了它们的性质,给出了M的非空子集成为蕴涵滤子及正蕴涵滤子的充要条件和M的蕴涵滤子成为正蕴涵滤子的充要条件.讨论了蕴涵滤子与正蕴涵滤子的关系,得到了M的每一个正蕴涵滤子都是蕴涵滤子,但反之不真.

The concept of implicative filters and positive implicative filters was introduced in MTL algebras M. The sufficient and necessary condition that non-empty subsets of M become （positive）implicative filters was given. The relation between implicative filters and positive implicative filters was discussed. The sufficient and necessary condition that implicative filters become positive implicative filters was given. We get that every positive implicative filter is an implicative filter, but the converse is not true.