模糊赋范线性空间的0-范数  

0-Norm of Fuzzy Normed Linear Space

作　　者：张入化 蒋浩 

机构地区：[1]西华大学理学院,四川 成都

出　　处：《应用数学进展》2023年第6期2945-2950,共6页Advances in Applied Mathematics

摘　　要：本文基于T. Bag和S.K. Samanta于2003年建立的模糊赋范线性空间。它们定义的模糊范数所导出的α-范数集是关于α-单增的范数集族。基于模糊范数与α-范数的联系,本文给出了模糊范数所导出的0-范数的概念,研究了0-范数是否是范数、0-范数与下确界范数的关系,同时研究了点列依0-范数收敛与依模糊范数收敛的关系。This paper is based on the fuzzy normed linear space established by T. Bag and S.K. Samanta in 2003. The α-norms set derived by their definition is an ascending family of norms . Based on the connection between fuzzy norm and α-norm, we present the concept of 0-norm de-rived by the fuzzy norm. We study whether the 0-norm is the norm, and the relationship of 0-norm and lower boundary norm. And then we also study the relationship between the 0-norm conver-gence and the fuzzy norm convergence.

关 键 词：模糊赋范线性空间 0-范数 0-范收敛 0-闭集 

分 类 号：O17[理学—数学]