关键词: 模糊蕴涵, 下三角, 序和, 充要条件

Abstract: By using the method of ordinal sum, we investigated the  necessary and sufficient conditions for a general fuzzy implication to be a proper complement to linear transformations of a given family of fuzzy implications on a given family of lower triangular parts of subsquares in the unit square. We put all kinds of  lower triangular ordinal sum implications into a unified framework, and then gave the general form of construction of  lower triangular ordinal sums  of fuzzy implications.

Key words: fuzzy implication, lower triangular, ordinal sum,  , necessary , and sufficient condition