摘要
对于逻辑系统代数结构的研究,是一个十分重要的研究课题.近期提出的BL代数,R_0代数,MTL代数就是这个方向具有代表性的研究成果.本文讨论MTL代数的性质与结构,给出这种代数的几个特征定理,澄清这种代数与其它代数结构的关系.鉴于单位区间中由左连续t-范数诱导的剩余蕴涵与MTL代数的紧密联系,本文还考察了这种模糊蕴涵的特征性质.
In logic and algebra, the researches on some logical algebraic structures are important topics at all times. BL algebras, R0 algebras and MTL algebras which are proposed recently are representative results in this area. The present paper discusses properties and algebraic structures of MTL algebras. Several characteristic properties of MTL algebras are revealed, and relationships among MTL algebras and the related algebraic structures are clarified. Moreover, cations induced by left continuous t-norms are closely related to MTL algebras. characteristic properties of residual impliare investisgated in this paper since they
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2007年第6期1201-1206,共6页
Acta Mathematica Sinica：Chinese Series
基金
国家科技部973项目(2006CB708304)
国家自然科学基金(60475019)
