Abstract: In the present paper, the structure of a class of left-continuous triangular norms, namely, F-λ triangular norms, is discussed. Based on F-λ triangular norms, several new families of triangular norms and families of implication operators associated with them are given. It is proved that the logical system built by F-λ triangular norms is just the WNM logical system, relations between triangular norms of NM, NMG, Godel as well as RDP and F-λ ones are discussed respectively, from this, the fact that logical systems NM, NMG, Godel as well as RDP are all the axiomatic extension of WNM logical system is proved.

Key words: left-continuous triangular norms, regular implication operators, F-&lambda, triangular norms, WNM logical system

摘要： 讨论了一类左连续的三角模（即，F-λ三角模）的结构，基于F-λ三角模给出了几种新的三角模族及与之相伴随的蕴涵算子族。证明了用此类三角模所建立的逻辑系统正是WNM逻辑系统，讨论了NM，NMG，Godel及RDP三角模与F-λ三角模的关系，并由此出发证明了NM，NMG，Godel及RDP等逻辑系统都是WNM逻辑系统的扩张。

关键词: 左连续三角模, 正则蕴涵算子, F-&lambda, 三角模, WNM逻辑系统