L-集合套的蕴涵运算及应用  

The implication operation of L-nested systems and its applications

作　　者：张庆玲[1] 方进明[1] 

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《模糊系统与数学》2017年第2期70-74,共5页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11471297)

摘　　要：本文在完备剩余格L的格值环境下,我们探究并给出了具有独立计算意义的L集合套蕴涵运算的表达式,从而添补了关于L-集合套无内在蕴涵运算的空白。为了表明得到的L-集合套蕴涵运算表达式的合理性和理论价值,文中进一步给出了两方面的应用:其一是用L-集合套蕴涵运算表达式可界定L-集合套张量积运算的内在表达式,其二是在完备剩余格满足否定对合条件时,证得L-集合套的补运算恰好可用L-集合套蕴涵运算表达式自然地获得。In this paper, an implication operation of L- nested systems computed by using L- nested systems themselves is obtained, where L is a complete residuated lattice. To clarify the rationality and theoretical value of the implication operation obtained in the paper further, two applications of it are presented. In particular, a complement of L- nested systems in the literature is covered by using the implication operation in the lattice valued context of an negative involution complete residuated lattice.

关 键 词：完备剩余格 L-集合套 L-集合套的蕴涵运算 L-集合套的补运算 表现定理 

分 类 号：O159[理学—数学]