F-λ三角模的结构及其应用  

Structure of F-λ triangular norm and its application

作　　者：丁博[1] 李骏[1] 

机构地区：[1]兰州理工大学理学院,兰州730050

出　　处：《计算机工程与应用》2016年第4期1-5,共5页Computer Engineering and Applications

基　　金：国家自然科学基金(No.11261032)

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。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.

关 键 词：左连续三角模 正则蕴涵算子 F-λ三角模 WNM逻辑系统 

分 类 号：O141.1[理学—数学]