摘要
本文采用[1]中fuzzy线性泛函的定义,证明了fuzzy拓扑线性空间上fuzzy线性泛函连续性的几个等价命题和fuzzy线性泛函的Hahn-Banach延拓定理。给出了fuzzy拓扑线性空间上存在非零连续fuzzy线性泛函的一个充要条件,并证明了非平几的分离的局部凸fuzzy拓扑线性空间上存在足够多的非零连续fuzzy线性泛函。
In this per, the definition of fuzzy linear functional which was given in [1] is adopted. We prove the seceral equivalent propositions for continuity of fuzzy linear functional on fuzzy topologicallinear space and Hahn-Banach extension theorem of fuzzy linear functional. We also give a sufficient and necessary condition that ensures there exist non-zero continuous fuzzy linear functionals on a fuzzy topological linear space, and prove that there exist enough non-zero continuous fuzzy linear functionals on non-zero separate locally convez fuzzy topological linear space,
出处
《南京师大学报（自然科学版）》
CAS
CSCD
1990年第3期1-8,共8页
Journal of Nanjing Normal University(Natural Science Edition)
基金
江苏省教委自然科学基金
关键词
模糊线性泛函
H-B定理
连续性
Fuzzy topological linear space, locally convex fuzzy topological linear space, fuzzy linear functional, continuous fuzzy linear functional, Hahn-Banach extension theorem.
