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。
Abstract:
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.