中文摘要：

模糊蕴涵代数,在文献中简称为FI代数,最初由吴望名先生于1990年提出,至今已经有许多研究成果.文中综述有关FI代数的概念,性质等主要研究工作,同时给出这类代数的一些新的性质.重点强调构成格结构的FI代数,称之为模糊蕴涵格,简称为FI格.这类代数结构与模糊逻辑中几个重要的代数系统具有紧密的联系,文中将揭示这些联系,一些重要的模糊逻辑代数系统都是FI格类的子类.另外,所有正则FI格构成代数簇,即等式代数类.这个代数簇将在模糊逻辑与近似推理中发挥重要的作用.

英文摘要：

Fuzzy implication algebras,FI algebras for short,were proposed by Professor Wu Wangming in 1990.Up to now,there have been many papers on FI algebras,and a series of results about FI algebras have been reported.This paper mainly reviews researches on FI algebras：its concepts and properties,relationships between FI algebras and several classes of important fuzzy logical algebras such as residuated lattices,MTL algebras,BL algebras and Heyting algebras.Some new results are given. Owing to the importance of lattice structures for fuzzy logic,in this paper,we specially emphasize fuzzy implication lattices,FI lattices for short,a class of interesting FI algebras.It is proved that all regular FI lattices form an algebraic variety,i.e.,an equational class of algebras.Regular FI lattices will play important roles in both researches of fuzzy logic and approximate reasoning.