摘要
本文的目的是以完备的Heyting代数为取值格,对经典的凸系统及其相关性质进行推广。首先,我们给出了L-凸系统的定义及其诱导L-凸空间的方法;其次,定义了L-凸系统上L-偏凸保持映射的概念,并证明了其与诱导的L-凸空间上L-凸保持映射的等价性;最后,我们对L-凸系统的商结构进行了讨论。
The aim of this paper is to generalize the concept and properties of convex systems to fuzzy setting with a complete Heyting algebra as the truth value table. First, we present a definition of L- convex systems, and then introduce the notion of L-convexity spaces induced by L-convex systems. Also, a concept of partial convexity-preserving maps is introduced. It is proved that the partial convexity-preserving maps on L-convex systems are equivalent to the convexity-preserving maps on their induced L-convexity spaces. At last, we define and study quotient systems.
出处
《模糊系统与数学》
北大核心
2017年第1期18-23,共6页
Fuzzy Systems and Mathematics
基金
国家自然科学基金资助课题(11371002)
高等学校博士学科点专项科研基金(20131101110048)
关键词
L-凸系统
L-偏凸保持映射
商系统
L-convex System
L-partial Convexity-preserving Map
L-quotient System
